The Well Posedness for Nonhomogeneous Boussinesq Equations - Yan Liu (MDPI AG, 2021)
This paper is devoted to studying the Cauchy problem for non-homogeneous Boussinesq equations. We built the results on the critical Besov spaces <semantics>(θ,u)∈<msubsup>LT∞</msubsup>(<msubsup><mover accent="true">B˙</mover>p,1N/p</msubsup>)×<msubsup>LT∞</msubsup>(<msubsup><mover accent="true">B˙</mover>p,1N/p−1</msubsup>)⋂<msubsup>LT1</msubsup>(<msubsup><mover accent="true">B˙</mover>p,1N/p+1</msubsup>)</semantics> with <semantics>1<p<2N</semantics>. We proved the global existence of the solution when the initial velocity is small with respect to the viscosity, as well as the initial temperature approaches a positive constant. Furthermore, we proved the uniqueness for <semantics>1<p≤N</semantics>. Our results can been seen as a version of symmetry in Besov space for the Boussinesq equations.