5,737 research outputs found
Global L_2-solutions of stochastic Navier-Stokes equations
This paper concerns the Cauchy problem in R^d for the stochastic
Navier-Stokes equation \partial_tu=\Delta u-(u,\nabla)u-\nabla p+f(u)+
[(\sigma,\nabla)u-\nabla \tilde p+g(u)]\circ \dot W, u(0)=u_0,\qquad divu=0,
driven by white noise \dot W. Under minimal assumptions on regularity of the
coefficients and random forces, the existence of a global weak (martingale)
solution of the stochastic Navier-Stokes equation is proved. In the
two-dimensional case, the existence and pathwise uniqueness of a global strong
solution is shown. A Wiener chaos-based criterion for the existence and
uniqueness of a strong global solution of the Navier-Stokes equations is
established.Comment: Published at http://dx.doi.org/10.1214/009117904000000630 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition
Using a weak convergence approach, we prove a LPD for the solution of 2D
stochastic Navier Stokes equations when the viscosity converges to 0 and the
noise intensity is multiplied by the square root of the viscosity. Unlike
previous results on LDP for hydrodynamical models, the weak convergence is
proven by tightness properties of the distribution of the solution in
appropriate functional spaces
Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition
We consider the stochastic divergence-free continuity equations with
Ladyzhenskaya-Prodi-Serrin condition. Wellposedness is proved meanwhile
uniqueness may fail for the deterministic PDE. The main issue of uniqueness
realies on stochastic characteristic method and the generalized
Ito-Ventzel-Kunita formula. Moreover, we prove a stability property for the
solution with respect to the initial datum.Comment: To appears in Nonlinear Differential Equations and Applications NoDE
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