Date: April 5 - 6

Venue: E10-312, Yungu Campus

Ⅰ  Agenda

Ⅱ  Talks

1. 9:00-10:00, April 5, Saturday

Speaker: Quoc Hung Nguyễn, Chinese Academy of Sciences

Title: Recent Advancements in Landau Damping

Abstract: In this talk, I will present recent advancements in understanding Landau damping within the context of the Vlasov-Poisson system, focusing on a variety of equilibrium conditions, including rapidly decaying equilibrium and non-monotone, compactly supported equilibrium profiles. Landau damping, a fundamental phenomenon in plasma physics and kinetic theory, describes the gradual energy transfer from large-scale electromagnetic waves to particle distributions. I will discuss new insights into the structure of wave-particle interactions and the fundamental mechanisms governing plasma stability. Additionally, I will explore nonlinear Landau damping for the relativistic Vlasov-Poisson equation, highlighting the complexities introduced by relativistic effects and their impact on the damping process. This talk will provide both theoretical advancements and a deeper understanding of the underlying dynamics governing plasma behavior in these more generalized settings.

2. 10:00-11:00, April 5, Saturday

Speaker: Mikhail Korobkov, Fudan University

Title: TBA

Abstract: TBA

3. 11:00-12:00, April 5, Saturday

Speaker: Alexey Cheskidov, Westlake University

Title: TBA

Abstract: TBA

4. 9:00-10:00, April 6, Sunday

Speaker: Gaston Vergara Hermosilla, Westlake University

Title: On Variable Lebesgue Spaces and Generalized Nonlinear Heat Equations

Abstract: In this talk we will address some questions concerning the Cauchy problem for a generalized nonlinear heat equations considering as functional framework the variable Lebesgue spaces. More precisely, by mixing some structural properties of these spaces with decay estimates of the fractional heat kernel, we will able to prove two well-posedness results for these equations.

5. 10:00-11:00, April 6, Sunday

Speaker: Jeaheang Bang, Westlake University

Title: Self-Similar Solutions to the Stationary Navier-Stokes Equations in a Higher Dimensional Cone

Abstract: Self-similar solutions play an important role in understanding the regularity and asymptotic behavior of solutions to the Navier-Stokes equations. We recently showed that self-similar solutions to the stationary Navier-Stokes equations in an $n$-dimensional cone with the no-slip boundary condition except at the origin must be trivial when $n\geq 4$ under an additional assumption on some part of the vorticity.  As a corollary, one can show the triviality of axisymmetric self-similar solutions. It rules out boundary singularity, under the additional assumption, which even has finite Dirichlet energy when $n\geq 5$.  The main idea is to use the equation of the head pressure along with the radial component of the stationary Navier-Stokes equations.  This is a joint work with Changfeng Gui, Chunjing Xie, Yun Wang, and Hao Liu.

6. 11:00-12:00, April 6, Sunday

Speaker: Hoang Minh Le, Westlake University

Title: Absence of blow-up in a fully parabolic chemotaxis system with weak singular sensitivity and logistic source

Abstract: Chemotaxis models, which describe the movement of cells or microorganisms in response to chemical stimuli, play a crucial role in biology and medicine. It is well known that blow-up can occur in certain chemotaxis systems, such as the Keller-Segel model or models with singular sensitivity. In this talk, I will discuss the global solvability and boundedness of a chemotaxis system with weak singular sensitivity and a logistic source. I will briefly present the main results, showing that blow-up cannot occur in any spatial dimension, and highlight key analytical techniques. Finally, I will discuss some open questions for future research.