Two-dimensional Navier–Stokes equations driven by a space–time white noise
G Da Prato, A Debussche - Journal of Functional Analysis, 2002 - Elsevier
Journal of Functional Analysis, 2002•Elsevier
We study the two-dimensional Navier–Stokes equations with periodic boundary conditions
perturbed by a space–time white noise. It is shown that, although the solution is not
expected to be smooth, the nonlinear term can be defined without changing the equation.
We first construct a stationary martingale solution. Then, we prove that, for almost every
initial data with respect to a measure supported by negative spaces, there exists a unique
global solution in the strong probabilistic sense.
perturbed by a space–time white noise. It is shown that, although the solution is not
expected to be smooth, the nonlinear term can be defined without changing the equation.
We first construct a stationary martingale solution. Then, we prove that, for almost every
initial data with respect to a measure supported by negative spaces, there exists a unique
global solution in the strong probabilistic sense.
We study the two-dimensional Navier–Stokes equations with periodic boundary conditions perturbed by a space–time white noise. It is shown that, although the solution is not expected to be smooth, the nonlinear term can be defined without changing the equation. We first construct a stationary martingale solution.Then, we prove that, for almost every initial data with respect to a measure supported by negative spaces, there exists a unique global solution in the strong probabilistic sense.
Elsevier
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