MHD equations with regularity in one direction
type: Item
instance of: scholarly article
title: MHD equations with regularity in one direction
zbMATH Open document ID: 1311.35239
DOI: 10.1155/2014/213083
author: Zujin Zhang
published in: International Journal of Partial Differential Equations
publication date: 2015-03-27T00:00:00Z
review text: Summary: We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, \(\partial_3\mathbf{u}\in L^p(0,T;L^q(\mathbb {R}^3))\), with \(2/p+3/q=\gamma\in [1,3/2)\), \(3/\gamma \leq q\leq 1/(\gamma -1)\), then the solution is in fact smooth. This improves previous results greatly.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6420097
zbMATH Keywords: regularity
zbMATH Keywords: magneto-hydrodynamics (MHD) equations
Wikidata QID: Q59048960
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/213083
OpenAlex ID: W2143426789
cites work: Inéquations en thermoélasticité et magnétohydrodynamique
cites work: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
cites work: On the regularity of weak solutions to the magnetohydrodynamic equations
cites work: Remarks on regularities for the 3D MHD equations
cites work: Remarks on the breakdown of smooth solutions for the 3-D Euler equations
cites work: A new regularity class for the Navier-Stokes equations in \(\mathbb{R}^ n\)
cites work: Regularity criterion in terms of pressure for the Navier-Stokes equations
cites work: On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations
cites work: Backward uniqueness for parabolic equations
cites work: On the regularity criteria for weak solutions to the magnetohydrodynamic equations
cites work: The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
cites work: On the interior regularity of weak solutions of the Navier-Stokes equations
cites work: Regularity Criteria for the Generalized MHD Equations
cites work: Regularity results for weak solutions of the 3D MHD equations.
cites work: Some Serrin-type regularity criteria for weak solutions to the Navier-Stokes equations
cites work: Regularity criteria for the generalized viscous MHD equations
cites work: Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain
cites work: Sufficient conditions for the regularity to the 3D Navier-Stokes equations
cites work: Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
cites work: Regularity criteria for the three-dimensional Navier-Stokes equations
cites work: A new regularity criterion for the 3D Navier-Stokes equations via two entries of the velocity gradient tensor
cites work: Two new regularity criteria for the Navier-Stokes equations via two entries of the velocity Hessian tensor
cites work: A Serrin-type regularity criterion for the Navier-Stokes equations via one velocity component
cites work: Two new regularity criteria for the 3D Navier-Stokes equations via two entries of the velocity gradient tensor
cites work: A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component.
cites work: A new regularity criterion for weak solutions to the Navier-Stokes equations
cites work: On a regularity criterion for the Navier–Stokes equations involving gradient of one velocity component
cites work: On the regularity of the solutions of the Navier–Stokes equations via one velocity component
cites work: Two regularity criteria for the 3D MHD equations
cites work: Regularity criteria for the 3D MHD equations via one directional derivative of the pressure
cites work: A regularity criterion for the 3D magneto-micropolar fluid equations in Triebel-Lizorkin spaces
description: scientific article; zbMATH DE number 6420097