Displaying similar documents to “On the existence for the Cauchy-Neumann problem for the Stokes system in the L p -framework”

Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in ℝ n

Reinhard Farwig, Hermann Sohr (2009)

Czechoslovak Mathematical Journal

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For a bounded domain Ω ⊂ ℝ n , n ≥ 3 , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system - Δ u + u · ∇ u + ∇ p = f , div u = k , u | ∂ Ω = g with u ∈ L q , q ≥ n , and very general data classes for f , k , g such that u may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of...

The resolution of the Navier-Stokes equations in anisotropic spaces.

Dragos Iftimie (1999)

Revista Matemática Iberoamericana

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In this paper we prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are H in the i-th direction, δ + δ + δ = 1/2, -1/2 < δ < 1/2 and in a space which is L in the first two directions and B in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.

On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

Piotr Mucha, Wojciech Zajączkowski (2000)

Applicationes Mathematicae

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The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that u ∈ W r 2 , 1 ( Ω ˜ T ) with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the L p -approach the Lagrangian coordinates must be used....