Low regularity of non-L^2(R^n) local solutions to gMHD-alpha systems




Riva, Lorenza
Pennington, Nathan

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Texas State University, Department of Mathematics


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 is 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.



Generalized MHD-alpha, Local solution, Low regularity


Riva, L., & Pennington, N. (2020). Low regularity of non-L^2(R^n) local solutions to gMHD-alpha systems. <i>Electronic Journal of Differential Equations, 2020</i>(54), pp. 1-17.


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