The suitable weak solution for the Cauchy problem of the double-diffusive convection system

ABSTRACT

In this paper, we consider the existence of the suitable weak solutions for the Cauchy problem of the double-diffusive convection system in ${\mathbb{R}}^3$. We establish the global existence of the suitable weak solutions of the double-diffusive convection system, especially, we obtain some generalized energy estimates which will play a very important role in studying the partial regularity of the suitable weak solutions of the double-diffusive convection system.

KEYWORDS:

• Suitable weak solution
• double-diffusive convection
• Cauchy problem

AMS SUBJECT CLASSIFICATIONS:

• 35Q35
• 35D30
• 76D03

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSFC [grant number 11731014] and [grant number 11571254] and by China Postdoctoral Science Foundation [grant number 2017M620688].