Local strong solutions to the nonhomogeneous Bénard system with nonnegative density. (English) Zbl 1451.35147
Summary: We study the Cauchy problem of the nonhomogeneous Bénard system in the whole two-dimensional (2D) space, where the density is allowed to vanish initially. We prove that there exists a unique local strong solution. To compensate for the lack of integrability of the velocity in the whole space, a careful space weight is imposed on the initial density, which cannot decay too slowly in the far field.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 35D35 | Strong solutions to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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