A time-dependent perturbation solution from a steady state for Marangoni problem. (English) Zbl 1394.35376
Summary: In this article, based on the \(T\)-weakly continuous theory, we prove the existence of global weak solution of the 2D incompressible Marangoni problem, which is modelled by the Boussinesq equations omitting effect of buoyancy. Moreover, we show that such weak solution is unique, and which is a time-dependent perturbation solution from a steady state.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 76B03 | Existence, uniqueness, and regularity theory for incompressible inviscid fluids |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 35D30 | Weak solutions to PDEs |
| 35B20 | Perturbations in context of PDEs |
| 76R10 | Free convection |
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