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Strong solutions to the 2D Cauchy problem of density-dependent viscous Boussinesq equations with vacuum. (English) Zbl 1414.76021

Summary: This paper concerns the Cauchy problem of the density-dependent Boussinesq equations without dissipation term on the temperature equation on the whole space \(\mathbb{R}^2\) with vacuum as far field density. We show that there exists a unique local strong solution provided the initial density and the initial temperature decay not too slow at infinity. In particular, the initial data can be arbitrarily large and the initial density may contain vacuum states. Moreover, there is no need to require any Cho-Choe-Kim type compatibility conditions.
©2019 American Institute of Physics

MSC:

76E06 Convection in hydrodynamic stability
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35F10 Initial value problems for linear first-order PDEs
76E20 Stability and instability of geophysical and astrophysical flows
86A10 Meteorology and atmospheric physics
35Q35 PDEs in connection with fluid mechanics
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