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08 February 2025
 
  » arxiv » 1605.0439

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Global Well-posedness of the Incompressible Magnetohydrodynamics
Yuan Cai ; Zhen Lei ;
Date 2 May 2016
AbstractThis 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
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