BKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity

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dc.creatorLei, Zhen
dc.creatorZhou, Yi
dc.date2009-01-18
dc.date.accessioned2026-07-07T12:31:31Z
dc.date.available2026-07-07T12:31:31Z
dc.descriptionIn this paper we derive a criterion for the breakdown of classical solutions to the incompressible magnetohydrodynamic equations with zero viscosity and positive resistivity in $\mathbb{R}^3$. This result is analogous to the celebrated Beale-Kato-Majda's breakdown criterion for the inviscid Eluer equations of incompressible fluids. In $\mathbb{R}^2$ we establish global weak solutions to the magnetohydrodynamic equations with zero viscosity and positive resistivity for initial data in Sobolev space $H^1(\mathbb{R}^2)$.
dc.descriptionto appear in DCDS-A, 2009
dc.identifierhttps://arxiv.org/abs/0901.2683
dc.identifierhttp://arxiv.org/abs/0901.2683
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216468
dc.subjectAnalysis of PDEs
dc.subject35Q35
dc.titleBKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity
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