Well-posedness of the Navier - Stokes - Maxwell equations

Research output: Contribution to journalArticle

Abstract

We study the local and global well-posedness of a full system of magnetohydrodynamic equations. The system is a coupling of the incompressible Navier - Stokes equations with the Maxwell equations through the Lorentz force and Ohm's law for the current. We show the local existence of mild solutions for arbitrarily large data in a space similar to the scale-invariant spaces classically used for Navier - Stokes. These solutions are global if the initial data are small enough. Our results not only simplify and unify the proofs for the space dimensions 2 and 3, but also refine those in [8]. The main simplification comes from an a priori L t 2 (L x ) estimate for solutions of the forced Navier - Stokes equations.

Original languageEnglish (US)
Pages (from-to)71-86
Number of pages16
JournalRoyal Society of Edinburgh - Proceedings A
Volume144
Issue number1
DOIs
StatePublished - Feb 2014

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Navier-Stokes
Maxwell's equations
Well-posedness
Magnetohydrodynamic Equations
Global Well-posedness
Local Existence
Mild Solution
Scale Invariant
Large Data
Incompressible Navier-Stokes Equations
Simplification
Navier-Stokes Equations
Simplify
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Well-posedness of the Navier - Stokes - Maxwell equations. / Germain, Pierre; Ibrahim, Slim; Masmoudi, Nader.

In: Royal Society of Edinburgh - Proceedings A, Vol. 144, No. 1, 02.2014, p. 71-86.

Research output: Contribution to journalArticle

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