RIT on Applied PDE Archives for Fall 2021 to Spring 2022
Organizational meeting
When: Mon, August 31, 2020 - 3:00pmWhere: Online seminar -- Email Jacob Bedrossian for a zoom link
Speaker: Applied PDE group (University of Maryland, College Park) -
Escaping Wells and Related Content
When: Mon, September 14, 2020 - 3:00pmWhere: Online
Speaker: Nick Paskal (University of Maryland, College Park) -
Global well-posedness for focusing NLS on semiperiodic space
When: Mon, September 21, 2020 - 3:00pmWhere: Online
Speaker: Zehua Zhao (University of Maryland, College Park) -
An introduction to Geometric Measure Theory I
When: Mon, September 28, 2020 - 3:00pmWhere: Online
Speaker: Antonio De Rosa (University of Maryland, College Park) -
Abstract: Contact Jacob Bedrossian, jacob@math.umd.edu for zoom link
Existence and uniqueness of global solutions for the Vlasov-Poisson-Fokker-Planck system
When: Mon, October 5, 2020 - 3:00pmWhere: Online
Speaker: Stavros Papathanasiou (University of Maryland, College Park) -
Abstract: https://umd.zoom.us/j/98137029467?pwd=VmlXajFSY1MzNmhCeXR2VndEWWJQQT09
An introduction to Geometric Measure Theory II
When: Mon, October 12, 2020 - 3:30pmWhere: Online
Speaker: Antonio de Rosa (University of Maryland, College Park) -
Abstract: Zoom link: https://umd.zoom.us/j/98137029467?pwd=VmlXajFSY1MzNmhCeXR2VndEWWJQQT09
Passive scalar turbulence and Lagrangian chaos pt. I
When: Mon, October 19, 2020 - 3:00pmWhere: Online
Speaker: Jacob Bedrossian (University of Maryland) -
Abstract: https://umd.zoom.us/j/98137029467?pwd=VmlXajFSY1MzNmhCeXR2VndEWWJQQT09
Lagrangian chaos and passive scalar turbulence
When: Mon, October 26, 2020 - 3:00pmWhere: Online
Speaker: Jacob Bedrossian () -
Abstract: https://umd.zoom.us/j/98137029467?pwd=VmlXajFSY1MzNmhCeXR2VndEWWJQQT09
Introduction to fully nonlinear elliptic equations
When: Mon, November 2, 2020 - 3:00pmWhere: Online
Speaker: Yijing Wu (University of Maryland) -
Abstract: https://umd.zoom.us/j/98137029467?pwd=VmlXajFSY1MzNmhCeXR2VndEWWJQQT09
Equilibration of attraction-repulsion models in collective dynamics
When: Mon, November 9, 2020 - 3:00pmWhere: Online
Speaker: Ruiwen Shu (UMD) -
Abstract: In this talk I will discuss some recent results related to the large time behavior of first order models with pairwise attraction and repulsion. The first part concerns the Newtonian repulsion with confinement (joint work with Eitan Tadmor). We prove the uniqueness of steady states for convex radial confining potentials, and prove an algebraic equilibration rate by constructing a Lyapunov-type functional. The uniqueness result is extended to the attraction-repulsion case with Newtonian repulsion and near-quadratic attraction. The second part concerns general attraction-repulsion (joint work with Jose Carrillo). For potentials satisfying the linear interpolation convexity (LIC), we prove the radial symmetry of Wasserstein-$\infty$ local minimizers. With some further assumptions, we prove the uniqueness of Wasserstein-$\infty$ local minimizers. When applying to power-law potentials, it implies that the steady state constructed in Carrillo-Huang 16' is indeed the unique local minimizer.
https://umd.zoom.us/j/98137029467?pwd=VmlXajFSY1MzNmhCeXR2VndEWWJQQT09
Control problems in infinite dimensional spaces with applications to SPDE
When: Mon, November 16, 2020 - 3:00pmWhere: Zoom -- Email jacob@math.umd.edu for link
Speaker: Chi-Hao Wu (UMD) -
Abstract: In this talk I will talk about a framework for studying approximate controllability in infinite dimensional spaces. As an application, I will talk about how this framework can be used to deduce the topological irreducibility of SPDE, which is closely related to the unique ergodicity. This talk is based on the work by Glatt-Holtz, Herzog and Mattingly.
Fractional Stokes operator on a bounded domain: Relation to fractional Sobolev spaces
When: Mon, December 7, 2020 - 3:00pmWhere: Online
Speaker: Pranava Jayanti (University of Maryland, College Park) -
Organizational meeting
When: Mon, February 1, 2021 - 3:00pmWhere: Online seminar -- Email Antonio De Rosa for a zoom link
Speaker: Applied PDE group (University of Maryland, College Park) -
Introduction to Almgren-Pitts min-max theory
When: Mon, February 15, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Antonio De Rosa (UMD) - https://sites.google.com/view/antonioderosa/home
Abstract: I will present the Almgren-Pitts min-max theory to search for minimal hypersurfaces in a closed manifold .
Introduction to Velocity Averaging
When: Mon, February 22, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: David Levermore (UMD) -
Abstract: TBA
On the structure of a two fluid system with Coulomb interactions
When: Mon, March 1, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Manoussos Grillakis (UMD) -
Abstract: I will look at two fluids which interact via a non-local potential. There is a certain structure which allows us to compare smooth solutions to nearby rougher ones. The idea, due to C. Dafermos, is to use the energy of the difference as a measure of the distance between two solutions. I will explain what is the structure that allows you to do this and why this is a natural consequence of a Geometric principle. This is joint work (in progress) with A. Tzavaras.
Compensated compactness hyper-viscosity and open questions
When: Mon, March 8, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Eitan Tadmor (UMD) -
Abstract: I will describe how the compensated compactness theory of Tartar-Murat can be used in two separate cases, to construct solutions for nonlinear scalar conservation laws without spatial BV bounds.
The first case deals with 1D equations. The classical method is based on vanishing viscosity limits. I will focus on hyper-viscosity limits, showing that compensated compactness based on one entropy production bound yields convergence. The convergence of spectral viscosity and finite volume approximations are prototype examples for such BV-free constructions.
A second case deals with solutions of 2D scalar equations: I will show that a judicious choice of two entropies entropy bounds will suffice.
Rough Paths and Rough Integrals
When: Mon, March 22, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Ran Tao (UMD) -
Abstract: I will give a brief introduction to the concept of the rough path and the rough integral and how they are associated with controlled differential equations and stochastic differential equations
An isoperimetric problem with a competing nonlocal term
When: Mon, March 29, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Yijing Wu (UMD) -
Abstract: We are interested in the isoperimetric problem in which the classical perimeter competes with a nonlocal interaction term. While the perimeter tries to aggregate the set E into a ball, the nonlocal term has the opposite effect. This competition leads to a non trivial problem in which even the existence of minimizers is not obvious. We will discuss some results on the classical Gamow’s liquid drop model of an atomic nucleus, and the problem when the usual perimeter is competing with a nonlocal singular term comparable to a fractional perimeter.
BMO^{-1} and the Navier-Stokes equations
When: Mon, April 5, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Stavros Papathanasiou (UMD) -
Abstract: TBA
Dynamics of Particles on a Curve with Pairwise Hyper-singular Repulsion
When: Mon, April 12, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Ruiwen Shu (UMD) -
Abstract: We investigate the large time behavior of $N$ particles restricted to a smooth closed curve in $\mathbb{R}^d$ and subject to a gradient flow with respect to Euclidean hyper-singular repulsive Riesz $s$-energy with $s>1$. We show that regardless of their initial positions, for all $N$ and time $t$ large, their normalized Riesz $s$-energy will be close to the $N$-point minimal possible energy. Furthermore, the distribution of such particles will be close to uniform with respect to arclength measure along the curve.
Hormander's condition for hypoellipticity and Malliavin calculus
When: Mon, April 19, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Chi-Hao Wu (UMD) -
Abstract: TBA
Faraday waves in soft elastic solids
When: Mon, May 10, 2021 - 3:00pmWhere: Contact Antonio De Rosa
Speaker: Giulia Bevilacqua (Politecnico di Milano) -
Abstract: Recent experiments have observed the emergence of standing waves at the free surface of elastic bodies attached to a rigid oscillating substrate and subjected to critical values of forcing frequency and amplitude. This phenomenon, known as Faraday instability, is now well understood for viscous fluids but surprisingly eluded any theoretical explanation for soft solids.
In this talk, we characterize Faraday waves in soft incompressible slabs using the Floquet theory to study the onset of harmonic and subharmonic resonance eigenmodes. We consider a ground state corresponding to a finite homogeneous deformation of the elastic slab. We transform the incremental boundary value problem into an algebraic eigenvalue problem characterized by the three dimensionless parameters, that characterize the interplay of gravity, capillary and elastic waves. Remarkably, we found that Faraday instability in soft solids is characterized by a harmonic resonance in the physical range of the material parameters. This seminal result is in contrast to the subharmonic resonance that is known to characterize viscous fluids, and opens the path for using Faraday waves for a precise and robust experimental method that is able to distinguish solid-like from fluid-like responses of soft matter at different scales.