Kyungkeun Kang

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.

Asymptotic stability of harmonic maps under the Schrödinger flow

For Schr ¨ odinger maps from R 2 × R + to the 2-sphere S 2 , it is not known if finite energy solutions can form singularities (blow up) in finite time. We consider equivariant solutions with energy near the energy of the two-parameter family of equivariant harmonic maps. We prove that if the topological degree of the map is at least four, blowup does not occur, and global solutions converge (in a dispersive sense, i.e., scatter) to a fixed harmonic map as time tends to infinity. The proof uses, among other things, a time-dependent splitting of the solution, the generalized Hasimoto transform, and Strichartz (dispersive) estimates for a certain two space–dimensional linear Schr¨ odinger equation whose potential has critical power spatial singularity and decay. Along the way, we establish an energy-space local well-posedness result for which the existence time is determined by the length scale of a nearby harmonic map.

Magnetic resonance-based reconstruction method of conductivity and permittivity distributions at the Larmor frequency

Magnetic resonance electrical property tomography is a recent medical imaging modality for visualizing the electrical tissue properties of the human body using radio-frequency magnetic fields. It uses the fact that in magnetic resonance imaging systems the eddy currents induced by the radio-frequency magnetic fields reflect the conductivity (

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

sigma

Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion

) and permittivity (

A PRESSURE DISTRIBUTION IMAGING TECHNIQUE WITH A CONDUCTIVE MEMBRANE USING ELECTRICAL IMPEDANCE TOMOGRAPHY

epsilon

Identification of a free boundary arising in a magneto-hydrodynamics system

) distributions inside the tissues through Maxwells equations. The corresponding inverse problem consists of reconstructing the admittivity distribution (

Analysis of localized damping effects in channel flows with a periodic rough boundary

gamma=sigma+iomegaepsilon

On maximum modulus estimates of the navier–stokes equations with nonzero boundary data

) at the Larmor frequency (

Solvability for Stokes System in Hölder Spaces in Bounded domains and Its Applications

omega/2pi=