Title&Abstract

Junsik Bae (UNIST)

Title: FORMATION OF SINGULARITIES IN COLLISION-FREE HYDROMAGNETIC WAVES 

Abstract:

We consider a certain PDE system, introduced by Gardner and Morikawa, describing the dynamics of collision-free magnetized plasma. The model is derived from the two-species 3D Euler-Maxwell system under suitable assumptions. We propose some sufficient conditions that lead to C1 blow-up in finite time. This is a joint work with Junho Choi (KAIST) and Bongsuk Kwon (UNIST).

Namhyun Eun (KAIST)

Title: Uniqueness and Stability of Riemann Shocks to the full Euler system

Abstract:

In this talk, we will discuss the stability of a Riemann shock solution to the compressible Euler system, which is a self-similar entropy shock connecting two different constant states, in a physical class of vanishing viscosity limits. We focus on the 1D full Euler system and consider the Brenner-Navier-Stokes-Fourier system, an amendment of the Navier-Stokes-Fourier system, to describe the physical perturbation class. (This is a joint work with Moon-Jin Kang and Saehoon Eo.)

Hobin Lee (KAIST)

Title: Asymptotic behavior toward viscous shock for 1D boundary problem of barotropic Navier-Stokes equations

Abstract:

 In this talk, I will consider the compressible barotropic Navier-Stokes equations in a half-line and

study the time-asymptotic behavior toward the outgoing viscous shock wave. First, I will introduce the three boundary problems: impermeable wall, inflow, and outflow problems, where the velocity at the boundary is given as a constant state.

After that, I will deal with impermeable wall and inflow problems more specifically. For both problems, I studied the situation which is related that the asymptotic profile determined by the prescribed constant states at the boundary and far-fields is a viscous shock.

The solutions of NSE asymptotically converges to the shifted viscous shock profiles, under the condition that initial perturbation are small enough.

So, after the middle part of the talk, I will explain how did I solve this problem. Especially, my results are based on the method of `a-contraction with shifts'. 

Youngjae Lee (Seoul National University)

Title: Existence and orbital stability of rotating patches on a surface of revolution 

Abstract:

In this talk, we will consider the existence and stability of rotating patches, which is the simplest dynamics on a surface of revolution. The same phenomenon can already be observed on a 2D plane, due to the rotational symmetry present in the 2D plane. This symmetry provides a conservation law, making the rotating patch an energy maximizer, which can be used to demonstrate Arnold stability. 

Deokwoo Lim (Seoul National University)

Title: On global regularity of some bi-rotational Euler flows in R4

Abstract:

We consider incompressible Euler equations with bi-rotational symmetry and no-swirl condition in R 4 . Such solutions have rotational invariance with respect to two rotation axes. In this talk, we discuss local and global well-posedness of Yudovich-type solutions. The local existence follows from extending the work of Danchin [Uspekhi Mat. Nauk 62(2007), no.3, 73–94] for axisymmetric flows in R3 . The global existence is obtained if the local-in-time solution satisfies additional decay conditions near the axes and at infinity. This is a joint work with Kyudong Choi(UNIST) and In-Jee Jeong(SNU). 

Jaeyong Shin (Yonsei University)

Title: On magneto-vorticity field and global solutions in Hall magnetohydrodynamics 

Abstract:

We consider the incompressible Hall magnetohydrodynamics system (Hall MHD in short) describing electrically conducting fluids interacting with magnetic fields. At first, we discuss the regularity criterion of magneto-vorticity field, and its applications. Then, we show that the Hall MHD system with 2D variables is globally well-posed when the vertical component of the current density is initially small in L2. This talk is based on a joint work with Hantaek Bae (UNIST) and Kyungkeun Kang (Yonsei University). 

Wanyong Shim (UNIST)

Title: Stability of shock profiles for the Navier-Stokes-Poisson system

Abstract:

We consider the one-dimensional Navier-Stokes-Poisson (NSP) system which describes dynamics of positive ions in a collision-dominated plasma. The NSP system admits uniqe (up to translation) traveling wave solutions called shock profiles. Stability analysis for the waves has two main difficulties: (i) the associated linearized operator has zero eigenvalue, (ii) the zero is embedded in regions of the essential spectrum in the frequency space. We adopt "Pointwise semigroup method" to resolve these issues and establish asymptotic orbital stability in Lp, with sharp decay rates in time. 

Youngjin Sim (UNIST)

Title: Existence of Sadovskii vortex patch

Abstract:

The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of 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 the 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. This talk is based on the joint work with Prof. Kyudong Choi (UNIST) and Prof. Injee Jeong (SNU).