Stochastic generalized magnetohydrodynamics equations: well-posedness (original) (raw)
Related papers
Stochastic solution of space-time fractional diffusion equations
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to explicit solutions for space-time fractional diffusion equations with multiscaling space-fractional derivatives, and additional insight into the meaning of these equations.
Stochastic solutions for fractional Cauchy problems
2001
Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional derivative. Solutions to fractional Cauchy problems are obtained by subordinating the solution to the original Cauchy problem. Fractional Cauchy problems are useful in physics to model anomalous diffusion.
2004
In this paper we study stochastic evolution equations driven by a fractional white noise with arbitrary Hurst parameter in infinite dimension. We establish the existence and uniqueness of a mild solution for a nonlinear equation with multiplicative noise under Lipschitz condition by using a fixed point argument in an appropriate inductive limit space. In the linear case with additive noise a strong solution is obtained. Those results are applied to stochastic parabolic partial differential equations perturbed by a fractional white noise.
The stochastic wave equation with fractional noise: A random field approach
Stochastic Processes and Their Applications, 2010
We consider the linear stochastic wave equation with spatially homogenous Gaussian noise, which is fractional in time with index H > 1/2. We show that the necessary and sufficient condition for the existence of the solution is a relaxation of the condition obtained in [10], when the noise is white in time. Under this condition, we show that the solution is L 2 (Ω)-continuous. Similar results are obtained for the heat equation. Unlike the white noise case, the necessary and sufficient condition for the existence of the solution in the case of the heat equation is different (and more general) than the one obtained for the wave equation.
Stochastic generalized fractional HP equations and applications
2009
In this paper we established the condition for a curve to satisfy stochastic generalized fractional HP (Hamilton-Pontryagin) equations. These equations are described using Ito integral. We have also considered the case of stochastic generalized fractional Hamiltonian equations, for a hyperregular Lagrange function. From the stochastic generalized fractional Hamiltonian equations, Langevin generalized fractional equations were found and numerical simulations were done.
Osaka Journal of Mathematics, 2006
In this paper we study a class of stochastic partial differential equations in the whole space mathbbRd\mathbb{R}^{d}mathbbRd, with arbitrary dimension dgeq1d\geq 1dgeq1, driven by a Gaussian noise white in time and correlated in space. The differential operator is a fractional derivative operator. We show the existence, uniqueness and H\"{o}lder's regularity of the solution. Then by means of Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure.
On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space
International Journal of Mathematics and Mathematical Sciences, 2009
We study a class of fractional stochastic integrodifferential equations considered in a real Hilbert space. The existence and uniqueness of the Mild solutions of the considered problem is also studied. We also give an application for stochastic integropartial differential equations of fractional order.