Chaogui Zhang, Ph.D.
Science Center, Room 320
Science Center, 3rd floor
Department Name Change
The Board of Trustees officially approved the change of our department name to "the Department of Mathematics and Computer Science" at the April 2014 board meeting.
Invited SpeakerDr. Jiahong Wu, Oklahoma State University USA and Chung-Ang University, South Korea
Time: Monday, Mar. 17, 2014 1:00PM - 2:00PM
Location: CNHS Room 201
Title: Partial Differential Equations of Fluids with Partial or Fractional Dissipation
This talk presents recent results on the global regularity problem concerning several PDEs modeling fluids when only partial dissipation or fractional dissipation is involved. Attention is focused on the 2D Boussinesq equations and the 2D magneto-hydrodynamic (MHD) equations. The Boussinesq equations concerned here model geophysical flows such as atmospheric fronts and ocean circulations. Mathematically the 2D Boussinesq equations serve as a lower dimensional model of the 3D hydrodynamics equations. We review recent results on various cases of partial dissipation and presents most recent developments on the 2D Boussinesq equations with fractional dissipation. The MHD equations model electrically conducting fluids such as plasmas. The MHD equations can be difficult to analyze due to the nonlinear coupling between the induction equation and the Naver-Stokes equations with the Lorentz force. Global regularity results for several partial and fractional cases will be summarized. Especially small global solutions with velocity dissipation or damping will be described.