I. Prof. Kyungkeun Kang, Yonsei University 

KKL1 

Title: Local boundary regularity of the Stokes and Navier-Stokes equations in the half space

Abstract: We are concerned with the existence of singular solutions for Stokes and the Navier-Stokes equations in the half-space near the boundary caused by some non-smooth either boundary data or external forces. We show that normal derivatives of solutions or velocity itself could be unbounded for the Stokes and Navier-Stokes equations near boundary away from support of some specific singular data.

KKL2 

Title: Existence of weak solutions for nonlinear diffusion equations with drift term and some applications

Abstract: We are concerned with weak solutions of porous medium equations and fast diffusion equations with drift terms, when the drift satisfies scaling invariance depending on $L^q$ norm. As applications, we consider various nonlinear system of nonlinear diffusion equations whose known existence and regularity results are revisited.

II. Prof. Jihoon Lee, Chung-Ang University 

JHL1

Title: On some singular limit problems of PDEs arising from fluid mechanics I

Abstract: The singular limit problem in the context of the Navier-Stokes equations and related fluid mechanics is a rich area of research that explores how solutions behave as certain parameters approach limiting values. In this talk, we consider some examples of singular limit problems including incompressible limit and quasi-geostrophic and rotating fluids.

 JHL2

Title: On some singular limit problems of PDEs arising from fluid mechanics II

Abstract: In this talk, we consider the singular limit problem of the incompressible Euler-Maxwell equations(EM). If we regard the speed of the light tends to infinity, then the solution of (EM) converges to that of inviscid MHD equations(MHD) in some suitable function space with well-prepared initial data. Also we consider the nonconvergence of the solution of (EM) to that of (MHD) for ill-prepared initial data.