Well-posedness for fractional Navier-Stokes equations in the largest critical spaces \(\dot B_{\infty ,\infty}^{ -(2\beta - 1)} (\mathbb R^n)\). (English) Zbl 1236.35115
Summary: This note studies the well-posedness of the fractional Navier-Stokes equations in some supercritical Besov spaces as well as in the largest critical spaces \(\dot B_{\infty ,\infty}^{ -(2\beta - 1)} (\mathbb R^n)\) for \(\beta \in \)(1/2,1). Meanwhile, the well-posedness for fractional magnetohydrodynamics equations in these Besov spaces is also studied.
MSC:
| 35Q30 | Navier-Stokes equations |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 30H25 | Besov spaces and \(Q_p\)-spaces |
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