Analytical smoothing effect of solution for the boussinesq equations

2017/02/22 by Cheng, F, Changliang Xu, Xu, C. -J
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1702.06737

openalex publication_date 2017/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, 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 H 1-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equation admet exactly same smoothing effect properties of incompressible Navier-Stokes equations.

Citations

• On the global well-posedness for Boussinesq system
• Gevrey regularity for a class of dissipative equations with applications to decay
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Global regularity for the 2D Boussinesq equations with partial viscosity terms

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