Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation (Journal of Mathematical Study, 2016)
This paper studies the global existence and regularity of classical solutionsto the 2D incompressible magneto-micropolar equations with partial dissipation. Themagneto-micropolar equations model the motion of electrically conducting micropolarfluids in the presence of a magnetic field. When there is only partial dissipation, theglobal regularity problem can be quite difficult. We are able to single out three specialpartial dissipation cases and establish the global regularity for each case. As specialconsequences, the 2D Navier-Stokes equations, the 2D magnetohydrodynamic equations,and the 2D micropolar equations with several types of partial dissipation alwayspossess global classical solutions. The proofs of our main results rely on anisotropicSobolev type inequalities and suitable combination and cancellation of terms.
Keywords: Global regularity; magneto-micropolar equations; partial dissipation.