Acta Mathematica Scientia

, Volume 39, Issue 1, pp 165–179 | Cite as

Analytical Smoothing Effect of Solution for the Boussinesq Equations

  • Feng Cheng (程峰)Email author
  • Chaojiang Xu (徐超江)


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 

2010 MR Subject Classification

35Q35 35M30 76B03 


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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Feng Cheng (程峰)
    • 1
    Email author
  • Chaojiang Xu (徐超江)
    • 2
    • 3
  1. 1.Hubei Key Laboratory of Applied Mathematics; School of Mathematics and StatisticsHubei UniversityWuhanChina
  2. 2.School of Mathematics and StatisticsWuhan UniversityWuhanChina
  3. 3.Université de Rouen, CNRS UMR 6085Laboratoire de MathématiquesSaint-Etienne du RouvrayFrance

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