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 , 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 language||English (US)|
|Number of pages||17|
|Journal||Electronic Journal of Differential Equations|
|State||Published - 2020|
All Science Journal Classification (ASJC) codes