Global Weak Solutions for an Incompressible Charged Fluid with Multi-Scale Couplings - Initial-Boundary Value Problem

PDE Seminar
Tuesday, April 7, 2009 - 3:05pm for 1.5 hours (actually 80 minutes)
Skiles 255
Joseph Jerome – Northwestern University, Evanston
Michael Westdickenberg
The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the speaker in [Transport Theory Statist. Phys. 31 (2002), 333-366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for examining evolution equations. In this talk, the existence of a global distribution solution is proved to hold for the model, in the case of the initial-boundary value problem. Connection of the above analysis to significant applications is discussed. The solution obtained is quite rudimentary, and further progress would be expected in resolving issues of regularity.