Journal ArticleDOI
Global martingale solution for the stochastic Boussinesq system with zero dissipation
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In this article, the authors studied the two-dimensional stochastic Boussinesq system with zero dissipation and multiplicative noise, and showed the existence of a martingale solution by a priori estimates using stocho-calculus, and applications of Prokhorov's, Skorokhod's, and Martingale representation theorems.Abstract:
We study the two-dimensional stochastic Boussinesq system with zero dissipation and multiplicative noise. We show the existence of a martingale solution by a priori estimates using stochastic calculus, and applications of Prokhorov's, Skorokhod's, and martingale representation theorems. Due to the lack of dissipation, the proof requires higher regularity estimates, taking advantage of the structure of the nonlinear term. Moreover, we obtain the existence of the pressure term via an application of de Rham's theorem for processes.read more
Citations
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On the Navier-Stokes equations
TL;DR: In this paper, a criterion for the convergence of numerical solutions of Navier-Stokes equations in two dimensions under steady conditions is given, which applies to all cases, of steady viscous flow in 2D.
Journal ArticleDOI
On the Well-Posedness of Stochastic Boussinesq Equations with Transport Noise
TL;DR: In this paper, the authors established the existence and uniqueness of maximal strong solutions of the stochastic Boussinesq equations with transport noise in Sobolev spaces and constructed a blow-up criterion.
Journal ArticleDOI
Well-posedness of Hall-magnetohydrodynamics system forced by L $$\acute{\mathrm{e}}$$ e ´ vy noise
Kazuo Yamazaki,Manil T. Mohan +1 more
TL;DR: In this article, the authors established the existence and uniqueness of a local smooth solution to the Cauchy problem for the Hall-magnetohydrodynamics system that is inviscid, resistive, and forced by multiplicative noise in the three dimensional space.
References
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Jean Jacod,Albert N. Shiryaev +1 more
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
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Infinite-Dimensional Dynamical Systems in Mechanics and Physics
TL;DR: In this article, the authors give bounds on the number of degrees of freedom and the dimension of attractors of some physical systems, including inertial manifolds and slow manifolds.
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Navier-Stokes Equations: Theory and Numerical Analysis
TL;DR: This paper presents thediscretization of the Navier-Stokes Equations: General Stability and Convergence Theorems, and describes the development of the Curl Operator and its application to the Steady-State Naviers' Equations.