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Regularity and decay of 3D incompressible MHD equations with nonlinear damping terms. (English) Zbl 1316.35247
Summary: We prove the existence and uniqueness of global strong solutions to the Cauchy problem for 3D incompressible MHD equations with nonlinear damping terms. Moreover, the preliminary \(L^{2}\) decay for weak solutions is also established.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B35 Stability in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
35D35 Strong solutions to PDEs
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