Results 31 to 35 of about 2,138 (35)

Smooth or singular solutions to the Navier--Stokes system ? [PDF]

arXiv, 2002
The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (including stationary ones), and a pointwise loss of smoothness for solutions are proved in the same function space of ...
arxiv  

A probabilistic representation for the vorticity of a 3D viscous fluid and for general systems of parabolic equations [PDF]

arXiv, 2003
A probabilistic representation formula for general systems of linear parabolic equations, coupled only through the zero-order term, is given. On this basis, an implicit probabilistic representation for the vorticity in a 3D viscous fluid (described by the Navier-Stokes equations) is carefully analysed, and a theorem of local existence and uniqueness is
arxiv  

Note on the finite time singularities for the 3D Navier-Stokes equations [PDF]

arXiv, 2005
The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.
arxiv  

Regularity of transition semigroups associated to a 3D stochastic Navier-Stokes equation [PDF]

arXiv, 2006
A 3D stochastic Navier-Stokes equation with a suitable non degenerate additive noise is considered. The regularity in the initial conditions of every Markov transition kernel associated to the equation is studied by a simple direct approach. A by-product of the technique is the equivalence of all transition probabilities associated to every Markov ...
arxiv  

Existence of martingale and stationary suitable weak solutions for a stochastic Navier-Stokes system [PDF]

arXiv, 2006
The existence of suitable weak solutions of 3D Navier-Stokes equations, driven by a random body force, is proved. These solutions satisfy a local balance of energy. Moreover it is proved also the existence of a statistically stationary solution.
arxiv