Dongkwang Kim(UNIST)
Title : Global Existence and Blow-up in a Repulsive Chemotaxis-Consumption System
Abstract : Chemotaxis-consumption systems describe the collective movement of biological species governed by both chemotactic interactions and consumption dynamics. In this talk, we explore a repulsive chemotaxis-consumption model, including cases with additional fluid effects, and examine the conditions under which global boundedness or blow-up occurs, as determined by the interplay between diffusion and chemotactic sensitivity.
Yoonjung Lee(Yonsei University)
Title : Global smooth solutions to the irrotational Euler-Riesz system in 3D
Abstract : The compressible Euler system is one of physical models which obeys the hyperbolic conservation law with no dissipation. It is known that the pure compressible Euler flows generally blows up in a finite time though, a remarkable work of Y. Guo discovered that the Poisson interaction force makes some oscillation and leads to some dispersion such as the Klein-Gordon effect. Such dispersion prevents the singularity formation phenomenon for the Euler--Poisson system and allows us to construct a global irrotational solution in the three dimensional case. In this talk, we are interested in the Euler system with the Riesz potential in 3D. The Riesz interaction serves as a generalization to the Poisson case and has been extensively studied in the physics literature. We investigate a dispersion feature of the linearized Euler--Riesz system. Unlike the Euler-Poisson case, the main difficulty in constructing the global irrotational solution arises from the singularity of the nonlinearity. We would like to explain a strategy to control the singularity, motivated by the work of Y. Guo and B. Pausader for ion dynamics model and present the recent result of the global irrotational solution to the 3D Euler--Riesz system.
Youngjin Sim(UNIST)
Title : Existence and stability of the Sadovskii vortex patches, together with parameter growth of a simply connected vortex patch in the half-domain
Abstract : The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl–Batchelor theory and as the asymptotic state for vortex ring dynamics. In this talk, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse condition and an upper bound on the circulation. Then, using a concentrated-compactness method, we obtain the orbital stability of Sadovskii vortex patches together with a shift estimate. Based on the stability result, we prove the existence of a simply-connect vortex patch solution which stays close to Sadovskii vortex patches and experiences the linear-in-time growth of parameter.
Seungjae Lee(Seoul National University)
Title : To Be Updated.
Abstract : To Be Updated.