Local existence of strong solutions to the generalized Boussinesq equations

Abstract

This paper deals with the local existence and uniqueness of strong solutions for the generalized Boussinesq equations with fractional dissipation. As a corollary, we establish some regularity criteria to guarantee smoothness of solutions.

Keywords:

• Generalized Boussinesq equations
• local existence

AMS Subject Classifications:

• 35B65
• 35A01
• 35A02

Acknowledgements

We would like to thank the anonymous referees for their valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by NSFC [grant number 11101376]; ZJNSF [grant number LY15A010009]; Scientific Research Foundation of the Higher Education Institutions of Gansu Province [grant number 2015A-131]; TSNSF [grant number TSA1406].