Persistence of global well-posedness for the two dimensional Boussinesq system with non-homogeneous boundary

ABSTRACT

In this paper, we study the initial boundary value problem for the 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions, and prove that for any initial data $(u_0,{\mathit{\theta }}_0)$ in $H^{1+s}\times H^{1+s}$, where $s\in (0,1)$, the persistence of global well-posedness has been obtained.

KEYWORDS:

• Persistence of global well-posedness
• Boussinesq system
• initial boundary value problem
• non-homogeneous boundary conditions

AMS SUBJECT CLASSIFICATIONS:

• 35Q30
• 35B30
• 76D03

Acknowledgements

The authors thank the referee for useful suggestions which improved the exposition considerably.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was in part supported by Natural Science Foundation of China [No.11671075]; Natural Science Foundation of Shanghai with the [contract number 16ZR1402100]; the Fundamental Research Funds for the Central Universities with the [contract number SUSF-DH-D-2015085].