ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

doi:10.1007/s10473-019-0114-9

Abstract

Abstract: In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H¹-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

Key words: analyticity, smoothing effect of solutions, Boussinesq equation

Feng CHENG, Chaojiang XU. ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS[J].Acta mathematica scientia,Series B, 2019, 39(1): 165-179.

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