JOINT MATHEMATICS COLLOQUIUM

UNIVERSITY OF IDAHO

WASHINGTON STATE UNIVERSITY


Department of Mathematics

University of Idaho


Fall 2014

Thursday,  September 11, 3:30-4:20 pm, room TLC 145

Refreshments in Brink 305 at 3:00 pm

On the existence and smoothness problem of the  magnetohydrodynamics system

 

Kazuo Yamazaki


Department of Mathematics

Washington State University

Abstract

The mathematical analysis of the time-dependent nonlinear PDE in fluid mechanics remains a challenging problem. In this talk, we focus on three particular PDEs: the Navier-Stokes equations, magnetohydrodynamics and magneto-micropolar fluid systems. We study component reduction of sufficient condition for the solutions to these PDEs to remain smooth for all time or blow up in finite time which requires harmonic analysis tools. If time remains, we elaborate on the existence of weak martingale and stochastically strong solution when these PDEs have forcing terms that are multiplicative noise. We will also discuss new results and also open problems.