Global existence of classical solutions to the two-dimensional compressible Boussinesq equations in a square domain
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A Priori
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Abstract In this paper, we consider the initial boundary value problem of two-dimensional isentropic compressible Boussinesq equations with constant viscosity and thermal diffusivity in a square domain. Based on the time-independent lower-order and time-dependent higher-order a priori estimates, we prove that the classical solution exists globally in time provided the initial mass $\|\rho _{0}\|_{L^{1}}$ ∥ ρ 0 ∥ L 1 of the fluid is small. Here, we have no small requirements for the initial velocity and temperature.
2007 ◽
Vol 12
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pp. 3-20
1972 ◽
Vol 69
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pp. 287-293
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Vol 49
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pp. 373-402
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2013 ◽
Vol 2013
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pp. 1-8
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