Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
Hideo Kozono, Hermann Sohr (1999)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in ”
Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
A generalization of a theorem by Kato on Navier-Stokes equations.
Marco Cannone (1997)
Revista Matemática Iberoamericana
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We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in C([0,∞);L(R)). More precisely, we show that if the initial data are sufficiently oscillating, in a suitable Besov space, then Kato's solution exists globally. As a corollary to this result, we obtain a theory of existence of self-similar solutions for the Navier-Stokes equations.
Asymptotics and stability for global solutions to the Navier-Stokes equations
Isabelle Gallagher, Dragos Iftimie, Fabrice Planchon (2003)
Annales de l’institut Fourier
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We consider an a priori global strong solution to the Navier-Stokes equations. We prove it behaves like a small solution for large time. Combining this asymptotics with uniqueness and averaging in time properties, we obtain the stability of such a global solution.
On the regular solutions for some classes of Navier-Stokes equations
Y. Ebihara, L.A. Medeiros (1988)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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.