The Experts below are selected from a list of 4371 Experts worldwide ranked by ideXlab platform
Dejun Luo - One of the best experts on this subject based on the ideXlab platform.
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Stochastic mSQG equations with multiplicative transport noises: white noise Solutions and scaling limit
arXiv: Probability, 2020Co-Authors: Dejun Luo, Rongchan ZhuAbstract:We consider the modified Surface Quasi-Geostrophic (mSQG) equation on the 2D torus $\mathbb{T}^2$, perturbed by multiplicative transport noise. The equation admits the white noise measure on $\mathbb{T}^2$ as the invariant measure. We first prove the existence of white noise Solutions to the stochastic equation via the method of point vortex approximation, then, under a suitable scaling limit of the noise, we show that the Solutions converge weakly to the Unique Stationary Solution of the dissipative mSQG equation driven by space-time white noise. The weak Uniqueness of the latter equation is also proved by following Gubinelli and Perkowski's approach in \cite{GP-18}.
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Convergence of transport noise to Ornstein–Uhlenbeck for 2D Euler equations under the enstrophy measure
The Annals of Probability, 2020Co-Authors: Franco Flandoli, Dejun LuoAbstract:We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable transport type noise and has white noise initial condition. It is shown that Stationary Solutions of this equation converge to the Unique Stationary Solution of the 2D Navier–Stokes equation driven by the space-time white noise.
Jean Dolbeault - One of the best experts on this subject based on the ideXlab platform.
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Relative Entropies for Kinetic Equations in Bounded Domains (Irreversibility, Stationary Solutions, Uniqueness)
Archive for Rational Mechanics and Analysis, 2003Co-Authors: Naoufel Ben Abdallah, Jean DolbeaultAbstract:The relative-entropy method describes the irreversibility of the Vlasov-Poisson and Vlasov-Boltzmann-Poisson systems in bounded domains with incoming boundary conditions. Uniform-in-time estimates are deduced from the entropy. In some cases, these estimates are sufficient to prove the convergence of the Solution to a Unique Stationary Solution, as time goes to infinity. The method is also used to analyse other types of boundary conditions such as mass- and energy-preserving diffuse-reflection boundary conditions, and to prove the Uniqueness of Stationary Solutions for some special collision terms.
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Relative entropies for the Vlasov–Poisson system in bounded domains
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000Co-Authors: Naoufel Ben Abdallah, Jean DolbeaultAbstract:Abstract Using relative entropies we study irreversibility for the Vlasov–Poisson system with injection conditions on the boundary with or without collisions. If the Solution converges for large times, this allows to deduce that the limit has a given trace on the boundary. In the one-dimensional collisionless case and under strong regularity assumptions, this is possible only for the Unique Stationary Solution.
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On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials
Differential and Integral Equations, 1995Co-Authors: François Bouchut, Jean DolbeaultAbstract:We prove that the Solution of the Vlasov-Fokker-Planck equation converges to the Unique Stationary Solution with same mass as time tends to infinity. The same result holds in the repulsive coulombic case for the Vlasov-Poisson-Fokker-Planck system; the newtonian attractive case is also studied. We establish positive and negative answers to the question of existence of a Stationary Solution for the last problem by examining the Poisson-Boltzmann equation.
Jonathan C Mattingly - One of the best experts on this subject based on the ideXlab platform.
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ergodicity of 2d navier stokes equations with random forcing and large viscosity
Communications in Mathematical Physics, 1999Co-Authors: Jonathan C MattinglyAbstract:The stochastically forced, two-dimensional, incompressable Navier–Stokes equations are shown to possess an Unique invariant measure if the viscosity is taken large enough. This result follows from a stronger result showing that at high viscosity there is a Unique Stationary Solution which attracts Solutions started from arbitrary initial conditions. That is to say, the system has a trivial random attractor. Along the way, results controling the expectation and averaging time of the energy and enstrophy are given.
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Ergodicity of 2D Navier–Stokes Equations with¶Random Forcing and Large Viscosity
Communications in Mathematical Physics, 1999Co-Authors: Jonathan C MattinglyAbstract:The stochastically forced, two-dimensional, incompressable Navier–Stokes equations are shown to possess an Unique invariant measure if the viscosity is taken large enough. This result follows from a stronger result showing that at high viscosity there is a Unique Stationary Solution which attracts Solutions started from arbitrary initial conditions. That is to say, the system has a trivial random attractor. Along the way, results controling the expectation and averaging time of the energy and enstrophy are given.
Franco Flandoli - One of the best experts on this subject based on the ideXlab platform.
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Convergence of transport noise to Ornstein–Uhlenbeck for 2D Euler equations under the enstrophy measure
The Annals of Probability, 2020Co-Authors: Franco Flandoli, Dejun LuoAbstract:We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable transport type noise and has white noise initial condition. It is shown that Stationary Solutions of this equation converge to the Unique Stationary Solution of the 2D Navier–Stokes equation driven by the space-time white noise.
Wenqiang Zhao - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic behavior of stochastic p-Laplacian-type equation with multiplicative noise
Boundary Value Problems, 2012Co-Authors: Wenqiang ZhaoAbstract:The Unique existence of Solutions to stochastic p-Laplacian-type equation with forced term satisfying some growth and dissipative conditions is established for the initial value in . The generation of a continuous random dynamical system and the existence of a random attractor for stochastic p-Laplacian-type equation driven by multiplicative noise are obtained. Furthermore, we obtain a random attractor consisting of a single point and thus the system possesses a Unique Stationary Solution. MSC:60H15, 35B40, 35B41.
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Existence of Random Attractors for a -Laplacian-Type Equation with Additive Noise
Abstract and Applied Analysis, 2011Co-Authors: Wenqiang ZhaoAbstract:We first establish the existence and Uniqueness of a Solution for a stochastic
