Symmetry (Nov 2021)
The Well Posedness for Nonhomogeneous Boussinesq Equations
Abstract
This paper is devoted to studying the Cauchy problem for non-homogeneous Boussinesq equations. We built the results on the critical Besov spaces (θ,u)∈LT∞(B˙p,1N/p)×LT∞(B˙p,1N/p−1)⋂LT1(B˙p,1N/p+1) with 1p2N. 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 1p≤N. Our results can been seen as a version of symmetry in Besov space for the Boussinesq equations.
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