Initial Boundary Value Problem for Two-Dimensional Viscous Boussinesq Equations

• DOI: 10.1007/s00205-010-0357-z
• Publication Date: 2010-09-06T14:15:36Z
• Authors: Ming-Jun Lai; Ronghua Pan; Kun Zhao
• Keywords: 0101 mathematics; 01 natural sciences

We study the initial boundary value problem of two-dimensional viscous Boussinesq equations over a bounded domain with smooth boundary. We show that the equations have a unique classical solution for H 3 initial data and the no-slip boundary condition. In addition, we show that the kinetic energy is uniformly bounded in time.