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Article overview
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Global Well-posedness of the Incompressible Magnetohydrodynamics | Yuan Cai
; Zhen Lei
; | Date: |
2 May 2016 | Abstract: | This paper studies the Cauchy problem of the incompressible
magnetohydrodynamic systems with or without viscosity $
u$. Under the
assumption that the initial velocity field and the displacement of the initial
magnetic field from a non-zero constant are sufficiently small in certain
weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed
for all $
u geq 0$ and all space dimension $n geq 2$. Such a result holds
true uniformly in nonnegative viscosity parameter. The proof is based on the
inherent strong null structure of the systems which was first introduced for
incompressible elastodynamics by the second author in cite{Lei14} and
Alinhac’s ghost weight technique. | Source: | arXiv, 1605.0439 | Services: | Forum | Review | PDF | Favorites |
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