Global Well-Posedness of the Incompressible Magnetohydrodynamics
By Yuan Cai, Zhen Lei. Archive for Rational Mechanics and Analysis, 2016
166 citations recorded by the source corpus.
This paper studies the Cauchy problem of the incompressible magnetohydro dynamic systems with or without viscosity ν. Under the assumption that the initial velocity field and the displacement of the initialmagnetic field froma non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all ν ≧ 0 and all spaces with dimension n ≧ 2. Such a result holds true uniformly in nonnegative viscosity parameters. The proof is based on the inherent strong null structure of the systems introduced by Lei (Commun Pure Appl Math 69(11):2072–2106, 2016) and the ghost weight technique introduced by Alinhac (Invent Math 145(3):597–618, 2001).
Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b29ee0fd80207e492aa769ec5178d95c07ad2437
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In Applied Mathematics
In Computational Mechanics
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Citations in the corpus
- Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium (2019, background): “The nonlinear stability for the ideal MHD equations was established in several beautiful papers [2,6,22,33,41].”