|
| TIME |
SPEAKER |
TITLE |
HOST |
October 4
In-person (also available on zoom), MW154+Zoom
| Juraj Foldes
(Virginia)
Zoom Link |
Singular radial solutions for super-critical Keller-Segel and Lin-Ni-Takagi equation |
Lam |
October 18
10:20-11:20 Virtual Only
| Robin Ming Chen
(Pittsburgh)
Zoom Link |
Orbital stability for internal waves |
Lam/Lou |
October 25
10:20-11:20 Virtual Only
| Andrej Zlatos
(UC San Diego)
Zoom Link |
On Universal Mixers |
Lam/Lou |
November 16; 2:00-2:55pm
Joint with Analysis Seminar
Note special time and date.
URL will be sent via announcement email on Nov 11.
| Prerona Dutta
(OSU)
Analysis Zoom Link
Password:Analysis
|
Metric entropy for generalized BV functions |
|
November 29
| Parisa Fatheddin
(OSU) |
Asymptotic behavior of stochastic Navier-Stokes and Schrodinger equations |
|
Abstracts
Juraj Folds, U Virginia (Oct 4, 2021)
Title: Singular radial solutions for super-critical Keller-Segel and Lin-Ni-Takagi equation
Abstract: We will discuss singular radially symmetric solution of the stationary Keller-Segel and Lin-Ni-Takagi equation, that is, an elliptic equation with exponential or power nonlinearity, which is super-critical in dimension bigger than 2. The solutions are unbounded at the origin, and we show that they describe the asymptotics of bifurcation branches of regular solutions. In particular, we will prove that for any ball and any positive k, there is a singular solution that satisfies Neumann boundary condition and oscillates at least k times around the constant equilibrium. Moreover, we will show that in dimension 3 ≤ N ≤ 9 there are regular solutions satisfying Neumann boundary conditions that are close to singular ones. Hence, it follows that there exist regular solutions on any ball with arbitrarily fast oscillations.
This is a joint work with Denis Bonheure (Université libre de Bruxelles) and Jean-Baptiste Casteras (Universidade de Lisboa).
Robin Ming Chen, U Pittsburgh (Oct 18, 2021)
Title: Orbital stability for internal waves
Abstract: I will discuss the nonlinear stability of capillary-gravity waves propagating along the interface dividing two immiscible fluid layers of finite depth. The motion in both regions is governed by the incompressible and irrotational Euler equations, with the density of each fluid being constant but distinct. We prove that for supercritical surface tension, all known small-amplitude localized waves are (conditionally) orbitally stable in the natural energy space. Moreover, the trivial solution is shown to be conditionally stable when the Bond and Froude numbers lie in a certain unbounded parameter region. For the near critical surface tension regime, we show that one can infer conditional orbital stability or orbital instability of small-amplitude traveling waves solutions to the full Euler system from considerations of a dispersive PDE similar to the steady Kawahara equation. This is joint work with S. Walsh.
Andrej Zlatos, UC San Diego (Oct 25, 2021)
Title: On Universal Mixers
Abstract: I will present a construction of universal mixers in all dimensions, that is, incompressible flows that asymptotically mix arbitrarily well general solutions to the corresponding transport equation. While no universal mixer can have a uniform mixing rate for all measurable initial data, these flows are also almost universal exponential mixers in the sense that they do achieve exponential-in-time mixing (which is the optimal rate) for all initial data with at least some degree of regularity. The constructed flows are time-dependent with an alternating cellular structure, and exist on tori as well as on bounded domains in Euclidean spaces. I will also present numerical evidence of exponential mixing by a different class of flows, alternating shear flows on two-dimensional tori.
Prerona Dutta, Ohio State (Nov 15, 2021)
Title: Metric entropy for generalized BV functions
Abstract: Inspired by a question posed by Lax in 2002, the study of metric entropy for nonlinear partial differential equations has received increasing attention in recent years. This talk demonstrates methods to obtain sharp upper and lower bounds on the metric entropy for a class of bounded total generalized variation functions taking values in a general totally bounded metric space. Thereafter we use this result to establish metric entropy estimates for the set of entropy admissible weak solutions to a scalar conservation law with weak genuinely nonlinear flux. Estimates of this type could provide a measure of the order of resolution of a numerical method required to solve the equation.
Parisa Fatheddin, Ohio State (Nov 15, 2021)
Title: Asymptotic behavior of stochastic Navier-Stokes and Schrodinger equations
Abstract: We consider the asymptotic limits of two dimensional incompressible stochastic Navier Stokes equation and one dimensional stochastic Schrodinger equation. These limits include large and moderate deviations, central limit theorem, and the law of the iterated logarithm. For large and moderate deviations, we will discuss both the Azencott method and the weak convergence approach and show how they can be used to derive the Strassen's compact law of the iterated logarithm. The exit problem will also be given as an application.
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