1,721,102 research outputs found
Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise
No full textWe prove ergodicity of the finite dimensional approximations of the three dimensional Navier–Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found that imply the ergodicity. The convergence rate to the unique invariant measure is shown to be exponential
Uniqueness and blow-up for a stochastic viscous dyadic model
Full text linkWe consider the dyadic model with viscosity and additive Gaussian noise as a simplified version of the stochastic Navier-Stokes equations, with the purpose of studying uniqueness and emergence of singularities. We prove path-wise uniqueness and absence of blow-up in the intermediate intensity of the non-linearity, morally corresponding to the 3D case, and blow-up for stronger intensity. Moreover, blow-up happens with probability one for regular initial data
Lototsky-Schnabl operators associated with a strictly elliptic differential operator and their corresponding Feller semigroup
No full textGiven an open bounded convex subset of , a strictly elliptic differential operator and a continuous function , and denoted with the Dirichlet operator associated with , the Lototsky-Schnabl operators associated with and are investigated. In particular, conditions are established which ensure the existence of a Feller semigroup represented by limit of powers of these operators. Then the analytic expression of the infinitesimal generator is determined and some properties of the semigroup are deduced. Finally, the saturation class of Lototsky-Schnabl operators is determined
Hölder regularity of the densities for the Navier-Stokes equations with noise
Full text linkWe prove that the densities of the finite dimensional projections of weak solutions of the Navier--Stokes equations driven by Gaussian noise are bounded and Holder continuous, thus improving the results of Debussche and Romito (2014).
The proof is based on analytical estimates on a conditioned Fokker--Planck equation solved by the density, that has a ``non--local'' term that takes into account the influence of the rest of the infinite dimensional dynamics over the finite subspace under observation
Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise
No full textWe prove that every Markov solution to the three dimensional Navier-Stokes equations with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast.
Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance
Some examples of singular fluid flows
No full textWe show, by an explicit construction, the existence of solutions to the Stokes system in dimension three that are singular on a fractal set. The singular points are understood in the sense given by Caffarelli, Kohn and Nirenberg (1982). As an application, we show the existence of suitable weak solutions to the Navier-Stokes equations, driven by rough forces, that are singular on a fractal set
Existence of martingale and stationary suitable weak solutions for a stochastic Navier-Stokes system
No full textThe 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. Existence of statistically stationary solutions is also proved
Random interfaces and the numerical discretization of the 1D stochastic Allen-Cahn problem
No full textThe uniqueness of weak solutions of the globally modified Navier-Stokes equations
No full textWe prove uniqueness for the globally modified Navier-Stokes equations recently introduced by Caraballo, Real and Kloeden [CarReaKlo06] for initial conditions in the space H of square-summable divergence-free vector fields
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