Low regularity of non-l2(ℝn) local solutions to GMHD-α systems

Lorenzo Riva, Nathan Pennington

Research output: Contribution to journalArticlepeer-review

Abstract

The Magneto-Hydrodynamic (MHD) system of equations governs viscous fluids subject to a magnetic field and is derived via a coupling of the Navier-Stokes equations and Maxwell’s equations. Recently it has become common to study generalizations of fluids-based differential equations. Here we consider the generalized Magneto-Hydrodynamic alpha (gMHD-α) system, which differs from the original MHD system by including an additional non-linear terms (indexed by α), and replacing the Laplace operators by more general Fourier multipliers with symbols of the form −|ξ|γ /g(|ξ|). In [8], the problem was considered with initial data in the Sobolev space Hs,2(ℝn) with n ≥ 3. Here we consider the problem with initial data in Hs,p(ℝn) with n ≥ 3 and p > 2. Our goal is to minimizing the regularity required for obtaining uniqueness of a solution.

Original languageEnglish (US)
Article number54
Pages (from-to)1-17
Number of pages17
JournalElectronic Journal of Differential Equations
Volume2020
StatePublished - 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

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