Myeongju Chae

Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations

We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove that solutions exist globally in time and upper bounds of temporal decays are obtained under the some smallness conditions of initial data.

Global classical solutions for a compressible fluid-particle interaction model

We consider a system coupling the compressible Navier–Stokes equations to the Vlasov–Fokker–Planck equation on three-dimensional torus. The coupling arises from a drag force exerted by each other. ...

On Mass Concentration for the L 2-Critical Nonlinear Schrödinger Equations

We consider the mass concentration phenomenon for the L 2-critical nonlinear Schrödinger equations. We show the mass concentration of blow-up solutions contained in space near the finite time. The new ingredient in this paper is a refinement of Strichartzs estimates with the mixed norm for 2 < q ≤ r.

Scattering Theory Below Energy for a Class of Hartree Type Equations

We prove the global existence and scattering for the Hartree-type equation in H s (ℝ3) the low regularity space s < 1. We follow the ideas in Colliander et al. (2004) to the Hartree-type nonlinearity, and also develop the theory of the classical multilinear operator modifying the L p estimate in Coifman and Meyer (1978).

ASYMPTOTIC BEHAVIORS OF SOLUTIONS FOR AN AEROTAXIS MODEL COUPLED TO FLUID EQUATIONS

We consider coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.

Mixed Norm Estimates of Schrödinger Waves and Their Applications

In this paper we establish mixed norm estimates of interactive Schrödinger waves and apply them to study smoothing properties and global well-posedness of the nonlinear Schrödinger equations with mass critical nonlinearity.

On mass concentration for the L2-critical nonlinear schrodinger equations

We consider the mass concentration phenomenon for the L 2-critical nonlinear Schrödinger equations. We show the mass concentration of blow-up solutions contained in space near the finite time. The new ingredient in this paper is a refinement of Strichartzs estimates with the mixed norm for 2 < q ≤ r.

Stability estimates of the Boltzmann equation in a half space

In this paper, we study the large-time behavior and the stability of continuous mild solutions to the Boltzmann equation in a half space. For this, we introduce two nonlinear functionals measuring future binary collisions and L 1 -distance. Through the time-decay estimates of these functionals and the pointwise estimate of the gain part of the collision operator, we show that continuous mild solutions approach to collision free flows time-asymptotically in L 1 , and L 1 -distance at time t is uniformly bounded by that of corresponding initial data, when initial datum is a small perturbation of the vacuum.

Semi-nonrelativistic limit of the Chern-Simons-Higgs system

The semi-nonrelativistic limit of Chern–Simons–Higgs system is considered. We obtain several uniform estimates with respect to the light speed c and show the convergence of the solution of Chern–Simons–Higgs system to the solution of Chern–Simons–Schrodinger equations.

On Mass Concentration for theL2-Critical Nonlinear Schrödinger Equations

We consider the mass concentration phenomenon for the L 2-critical nonlinear Schrödinger equations. We show the mass concentration of blow-up solutions contained in space near the finite time. The new ingredient in this paper is a refinement of Strichartzs estimates with the mixed norm for 2 < q ≤ r.