Well-posedness of the MHD boundary layer system in Gevrey function space without Structural Assumption

Li, Weixi; Yang, Tong

doi:10.48550/arxiv.2009.06513

Cited by 1 publication

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References 44 publications

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“…Yang [13] with Gevrey index up to 3/2, and it remains interesting to relax the Gevrey index therein to 2 inspired the previous works of [4,11] on the well-posedness for the Prandtl equations in Gevrey space with optimal index 2. • Under the structural assumption that the tangential magnetic field dominates, i.e., f = 0, the well-posedness in weighted Sobolev space was established by Liu-Xie-Yang [17] and Liu-Wang-Xie-Yang [15] without Oleinik's monotonicity assumption, where the two cases that with both viscosity and resistivity and with only viscosity are considered, respectively.…”

Section: Introductionmentioning

confidence: 95%

Well-posedness in Sobolev spaces of the two-dimensional MHD Boundary layer equations without viscosity

Li¹,

Xu²

2021

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We consider the two-dimensional MHD Boundary layer system without hydrodynamic viscosity, and establish the existence and uniqueness of solutions in Sobolev spaces under the assumption that the tangential component of magnetic fields dominates. This gives a complement to the previous works of Liu-Xie-Yang [Comm. Pure Appl. Math. 72 (2019)] and Liu-Wang-Xie-Yang [J. Funct. Anal. 279 (2020)], where the well-posedness theory was established for the MHD boundary layer systems with both viscosity and resistivity and with viscosity only, respectively. We use the pseudo-differential calculation, to overcome a new difficulty arising from the treatment of boundary integrals due to the absence of the diffusion property for the velocity.

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