AIMS Mathematics, 2020, 5(4): 2869-2876. doi: 10.3934/math.2020184.

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On the dissipative solutions for the inviscid Boussinesq equations

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

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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Keywords Boussinesq equations; dissipative solution; weak solution

Citation: Feng Cheng. On the dissipative solutions for the inviscid Boussinesq equations. AIMS Mathematics, 2020, 5(4): 2869-2876. doi: 10.3934/math.2020184

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