Formation of small scales in nonlinear PDEs

Persistence of regularity and long time behavior of solutions for the Boussinesq equations

Weinan Wang

University of Southern California

We address the global persistence of Sobolev regularity for the 2D fractional Boussinesq equations and then we consider the long time behavior of solutions for the 2D Boussinesq equations in different domains, including \mathbb R^2, \mathbb T^2, bounded domain with Lions or Dirichlet boundary conditions.