Global strong solution to the 2D nonhomogeneous incompressible MHD system
By Xiangdi Huang, Yun Wang. 2012
149 citations recorded by the source corpus.
Abstract In this paper, we first prove the unique global strong solution with vacuum to the two-dimensional nonhomogeneous incompressible MHD system, as long as the initial data satisfies some compatibility condition. As a corollary, the global existence of strong solution with vacuum to the 2D nonhomogeneous incompressible Navier–Stokes equations is also established. Our main result improves all the previous results where the initial density need to be strictly positive. The key idea is to use some critical Sobolev inequality of logarithmic type, which is originally due to Brezis and Wainger (1980) [7] .
Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/897155a03d523b9fdec6733277c05d487879a403
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In Applied Mathematics
In Computational Mechanics
In Mathematical Physics
Citations in the corpus
- Global well-posedness for the incompressible Navier–Stokes equations with density-dependent viscosity coefficient (2015, background): “Huang and Wang [13] proved in dimension two that the local strong solution obtained in [6] is indeed a global one.”