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Global smooth solutions to the $$n$$-dimensional damped models of incompressible fluid mechanics with small initial datum. (English) Zbl 1311.35236
Summary: In this paper, we consider the $$n$$-dimensional ($$n\geq 2$$) damped models of incompressible fluid mechanics in Besov spaces and establish the global (in time) regularity of classical solutions provided that the initial data are suitable small.

##### 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 35Q86 PDEs in connection with geophysics 86A10 Meteorology and atmospheric physics 76E06 Convection in hydrodynamic stability
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