Displaying similar documents to “Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in ℝ 3 ”

A generalization of a theorem by Kato on Navier-Stokes equations.

Marco Cannone (1997)

Revista Matemática Iberoamericana

Similarity:

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

Similarity:

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.

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

Dragos Iftimie (1999)

Revista Matemática Iberoamericana

Similarity:

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.