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Deugoue, G.; Djoko, J. K.; Fouape, A. C.

On the convergence of solutions of globally modified magnetohydrodynamics equations with locally Lipschitz delays terms. (English) Zbl 1492.76146

Quaest. Math. 45, No. 4, 627-653 (2022).
Summary: Existence and uniqueness of strong solutions for the three dimensional system of globally modified magnetohydrodynamics equations with locally Lipschitz delays terms are established in this article. Galerkin’s method and Aubin Lions compactness theorem are the main mathematical tools we use to prove the existence result. Moreover, we prove that, from a sequence of weak solutions of globally modified magnetohydrodynamics equations with locally Lipschitz delays terms, we can extract a subsequence which converges in an adequate sense to a weak solution of three dimensional magnetohydrodynamics equations with locally Lipschitz delays terms.

Cited in 1 Document

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory

Keywords:

globally modified Navier-Stokes equations; strong solution; convergence; finite delay; existence; uniqueness; Galerkin method; Aubin-Lions compactness theorem
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