Displaying similar documents to “Wellposedness and stability results for the Navier-Stokes equations in 𝐑 3 ”

On the blow up criterion for the 2-D compressible Navier-Stokes equations

Lingyu Jiang, Yidong Wang (2010)

Czechoslovak Mathematical Journal

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Motivated by [10], we prove that the upper bound of the density function ρ controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.

The role of oscillations in the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations

Jean-Yves Chemin, Ping Zhang (2005-2006)

Séminaire Équations aux dérivées partielles

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Corresponding to the wellposedness result [] for the classical 3-D Navier-Stokes equations ( N S ν ) with initial data in the scaling invariant Besov space, ℬ p , ∞ - 1 + 3 p , here we consider a similar problem for the 3-D anisotropic Navier-Stokes equations ( A N S ν ) , where the vertical viscosity is zero. In order to do so, we first introduce the Besov-Sobolev type spaces, ℬ 4 - 1 2 , 1 2 and ℬ 4 - 1 2 , 1 2 ( T ) . Then with initial data in the scaling invariant space ℬ 4 - 1 2 , 1 2 , we prove the global wellposedness for ( A N S ν ) provided the norm of initial data is small...