Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Fall 2018-Spring 2019)
(PDE GA Seminar Schedule Fall 2019-Spring 2020)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===
+
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===
  
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==
+
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==
  
  
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!align="left" | title
 
!align="left" | title
 
!style="width:20%" align="left" | host(s)
 
!style="width:20%" align="left" | host(s)
 
 
|-   
 
|-   
|August 31 (FRIDAY),
+
|Sep 9
| Julian Lopez-Gomez (Complutense University of Madrid)
+
| Scott Smith (UW Madison)
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]
+
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]
| Rabinowitz
+
| Kim and Tran
 
+
|-
 +
|Sep 14-15
 +
|
 +
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html  ]]
 +
 +
|- 
 +
|Sep 23
 +
| Son Tu (UW Madison)
 +
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]
 +
| Kim and Tran
 +
|- 
 +
|Sep 28-29, VV901
 +
|  https://www.ki-net.umd.edu/content/conf?event_id=993
 +
|  |  Recent progress in analytical aspects of kinetic equations and related fluid models 
 +
 +
|- 
 +
|Oct 7
 +
| Jin Woo Jang (Postech)
 +
|[[#Speaker | TBA ]]
 +
| Kim
 
|-   
 
|-   
|September 10,
+
|Oct 14
| Hiroyoshi Mitake (University of Tokyo)
+
| Stefania Patrizi (UT Austin)
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]
+
|[[#Stefania Patrizi | TBA ]]
 
| Tran
 
| Tran
 
|-   
 
|-   
|September 12 and September 14,
+
|Oct 21
| Gunther Uhlmann (UWash)
+
| Claude Bardos (Université Paris Denis Diderot, France)
|[[#Gunther Uhlmann | TBA ]]
+
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]
 
| Li
 
| Li
 
|-   
 
|-   
|September 17,
+
|Oct 28
| Changyou Wang (Purdue)
+
| Albert Ai (UW Madison)
|[[#Changyou Wang Some recent results on mathematical analysis of Ericksen-Leslie System ]]
+
|[[#Albert Ai | TBA ]]
 +
| Ifrim
 +
|- 
 +
|Nov 4
 +
| Yunbai Cao (UW Madison)
 +
|[[#Yunbai Cao | TBA ]]
 +
| Kim and Tran
 +
|- 
 +
|Nov 11
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|Nov 18
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|-
 +
|Nov 25
 +
| Mathew Langford (UT Knoxville)
 +
|[[#Speaker | TBA ]]
 +
| Angenent
 +
|-  
 +
|-
 +
|Feb 17
 +
| Yannick Sire (JHU)
 +
|[[#Yannick Sire (JHU) | TBA ]]
 
| Tran
 
| Tran
|-
 
|Sep 28, Colloquium
 
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
 
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
 
| Thiffeault
 
 
|-   
 
|-   
|October 1,
+
|Feb 24
| Matthew Schrecker (UW)
+
| Speaker (Institute)
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]
+
|[[#Speaker | TBA ]]
| Kim and Tran
+
| Host
 +
|- 
 +
|March 2
 +
| Theodora Bourni (UT Knoxville)
 +
|[[#Speaker | TBA ]]
 +
| Angenent
 +
|- 
 +
|March 9
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 
|-   
 
|-   
|October 8,
+
|March 16
| Anna Mazzucato (PSU)
+
| No seminar (spring break)
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]
+
|[[#Speaker | TBA ]]
| Li and Kim
+
| Host
 
|-   
 
|-   
|October 15,
+
|March 23
| Lei Wu (Lehigh)
+
| Jared Speck (Vanderbilt)
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]
+
|[[#Jared Speck | TBA ]]
| Kim
+
| SCHRECKER
 
|-   
 
|-   
|October 22,
+
|March 30
| Annalaura Stingo (UCD)
+
| Speaker (Institute)
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]
+
|[[#Speaker | TBA ]]
| Mihaela Ifrim
+
| Host
 
|-   
 
|-   
|October 29,
+
|April 6
| Yeon-Eung Kim (UW)
+
| Speaker (Institute)
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]
+
|[[#Speaker | TBA ]]
| Kim and Tran
+
| Host
 
|-   
 
|-   
|November 5,
+
|April 13
| Albert Ai (UC Berkeley)
+
| Speaker (Institute)
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]
+
|[[#Speaker | TBA ]]
| Mihaela Ifrim
+
| Host
 
|-   
 
|-   
|Nov 7 (Wednesday), Colloquium
+
|April 20
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)
+
| Hyunju Kwon (IAS)
|[[#Nov 7: Luca Spolaor (MIT) |  (Log)-Epiperimetric Inequality and the Regularity of Variational Problems  ]]
+
|[[#Hyunju Kwon | TBA ]]
| Feldman
 
|-
 
|December 3,
 
| Trevor Leslie (UW)
 
|[[#Trevor Leslie | TBA ]]
 
| Kim and Tran
 
|-
 
|December 10,
 
|Serena Frederico (MIT)
 
|[[#Serena Frederico | TBA ]]
 
| Mihaela Ifrim
 
|-
 
|January 28,
 
|  ( )
 
|[[#  | TBA ]]
 
 
|-
 
|Time: TBD,
 
| Jessica Lin (McGill University)
 
|[[#Jessica Lin | TBA ]]
 
| Tran
 
|-   
 
|March 4
 
| Vladimir Sverak (Minnesota)
 
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]
 
 
| Kim
 
| Kim
|-  
+
|-   
|March 11
+
|April 27
| Jonathan Luk (Stanford)
+
| Speaker (Institute)
|[[#Jonathan Luk | TBA  ]]
+
|[[#Speaker | TBA ]]
| Kim
+
| Host
|-
 
|March 18,
 
| Spring recess (Mar 16-24, 2019)
 
|[[#  |  ]]
 
|  
 
|-
 
|April 29,
 
|   ( )
 
|[[# | TBA ]]
 
|
 
 
|}
 
|}
  
 
== Abstracts ==
 
== Abstracts ==
  
===Julian Lopez-Gomez===
+
===Scott Smith===
 
 
Title: The theorem of characterization of the Strong Maximum Principle
 
 
 
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes  a popular result of Berestycki, Nirenberg and Varadhan.
 
 
 
===Hiroyoshi Mitake===
 
Title: On approximation of time-fractional fully nonlinear equations
 
 
 
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.)
 
 
 
 
 
 
 
===Changyou Wang===
 
 
 
Title: Some recent results on mathematical analysis of Ericksen-Leslie System
 
 
 
Abstract: The Ericksen-Leslie system is the governing equation  that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.
 
 
 
===Matthew Schrecker===
 
 
 
Title: Finite energy methods for the 1D isentropic Euler equations
 
 
 
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.
 
 
 
===Anna Mazzucato===
 
 
 
Title: On the vanishing viscosity limit in incompressible flows
 
 
 
Abstract: I will discuss recent results on the  analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity  may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions.  I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.
 
 
 
===Lei Wu===
 
 
 
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects
 
 
 
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.
 
 
 
 
 
===Annalaura Stingo===
 
 
 
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D
 
 
 
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms »  .
 
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.
 
  
===Yeon-Eung Kim===
+
Title: Recent progress on singular, quasi-linear stochastic PDE
  
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties
+
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing .  These equations are ill-posed in the traditional sense of distribution theory.  They require flexibility in the notion of solution as well as new a priori bounds.  Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory.  This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.
  
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.
 
  
===Albert Ai===
+
===Son Tu===
  
Title: Low Regularity Solutions for Gravity Water Waves
+
Title: State-Constraint static Hamilton-Jacobi equations in nested domains
  
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.
+
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).

Latest revision as of 11:37, 19 September 2019

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Previous PDE/GA seminars

Tentative schedule for Fall 2020-Spring 2021

PDE GA Seminar Schedule Fall 2019-Spring 2020

date speaker title host(s)
Sep 9 Scott Smith (UW Madison) Recent progress on singular, quasi-linear stochastic PDE Kim and Tran
Sep 14-15 AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html
Sep 23 Son Tu (UW Madison) State-Constraint static Hamilton-Jacobi equations in nested domains Kim and Tran
Sep 28-29, VV901 https://www.ki-net.umd.edu/content/conf?event_id=993 Recent progress in analytical aspects of kinetic equations and related fluid models
Oct 7 Jin Woo Jang (Postech) TBA Kim
Oct 14 Stefania Patrizi (UT Austin) TBA Tran
Oct 21 Claude Bardos (Université Paris Denis Diderot, France) From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture Li
Oct 28 Albert Ai (UW Madison) TBA Ifrim
Nov 4 Yunbai Cao (UW Madison) TBA Kim and Tran
Nov 11 Speaker (Institute) TBA Host
Nov 18 Speaker (Institute) TBA Host
Nov 25 Mathew Langford (UT Knoxville) TBA Angenent
Feb 17 Yannick Sire (JHU) TBA Tran
Feb 24 Speaker (Institute) TBA Host
March 2 Theodora Bourni (UT Knoxville) TBA Angenent
March 9 Speaker (Institute) TBA Host
March 16 No seminar (spring break) TBA Host
March 23 Jared Speck (Vanderbilt) TBA SCHRECKER
March 30 Speaker (Institute) TBA Host
April 6 Speaker (Institute) TBA Host
April 13 Speaker (Institute) TBA Host
April 20 Hyunju Kwon (IAS) TBA Kim
April 27 Speaker (Institute) TBA Host

Abstracts

Scott Smith

Title: Recent progress on singular, quasi-linear stochastic PDE

Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.


Son Tu

Title: State-Constraint static Hamilton-Jacobi equations in nested domains

Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).