Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations
The authors derive some new equations which they call MHD-Leray-alpha equations, and which are similar to the MHD equations. For these equations, the authors prove the existence of a unique weak solution and a unique strong solution global in time. The authors also establish the Gevrey class of regularity when the initial data are smooth enough and the forces belong to a suitable Gevrey class. Moreover, it is shown that the solutions of the MHD-Leray-alpha equations converge to the solution of the MHD equations in a weak sense as a parameter in the new equations converges to zero. The proof is based on Faedo-Galerkin method and on Fourier series expansions.
scientific article; zbMATH DE number 5129647
scientific article