On the dissipative solutions for the inviscid Boussinesq equations

Feng Cheng; Feng Cheng

doi:10.3934/math.2020184

AIMS Mathematics

2020, Volume 5, Issue 4: 2869-2876. doi: 10.3934/math.2020184

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Research article

On the dissipative solutions for the inviscid Boussinesq equations

Feng Cheng ^,

Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, P. R. China

Received: 24 November 2019 Accepted: 11 February 2020 Published: 18 March 2020
MSC : 35A01, 35Q35, 76B03

In this paper, we study the dissipative solutions for the inviscid Boussinesq equations. It is shown that there is at least one dissipative solution for the inviscid incompressible Boussinesq equations. Moreover, if there is an unique strong solution then the dissipative solutions must coincide with the strong solution.
- Boussinesq equations,
- dissipative solution,
- weak solution
Citation: Feng Cheng. On the dissipative solutions for the inviscid Boussinesq equations[J]. AIMS Mathematics, 2020, 5(4): 2869-2876. doi: 10.3934/math.2020184

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Abstract

In this paper, we study the dissipative solutions for the inviscid Boussinesq equations. It is shown that there is at least one dissipative solution for the inviscid incompressible Boussinesq equations. Moreover, if there is an unique strong solution then the dissipative solutions must coincide with the strong solution.

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