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Optimale lokale Existenzsätze für die Gleichungen von Navier-Stokes. (German) Zbl 0552.35059

The paper is devoted to the local existence and the uniqueness of the solution of the Dirichlet-Cauchy problem for the non-stationary Navier- Stokes equations. Under some assumptions on the Cauchy data \(u_ 0\) and on the external forces f it is proved in an \(L^ q\) \((0,T;L^ q)\) theory, that a unique solution exists on an interval \((0,T^*)\), where \(T^*=T^*(u_ 0,f)\) and this solution has some special properties.
Reviewer: T.Petrila

MSC:

35Q30 Navier-Stokes equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
76D05 Navier-Stokes equations for incompressible viscous fluids
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References:

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