Multidimensional Stochastic Burgers Equation
نویسندگان
چکیده
We consider multidimensional stochastic Burgers equation on the torus T and the whole space R . In both cases we show that for positive viscosity ν > 0 there exists a unique strong global solution in L for p > d. In the case of torus we also establish a uniform in ν a priori estimate and consider a limit ν ↘ 0 for potential solutions. In the case of R uniform with respect to ν a priori estimate established if a Beale-Kato-Majda type condition is satisfied. CONTENTS
منابع مشابه
Stochastic PDEs in Turbulence Theory
This paper reviews the recent progress on stochastic PDEs arising from different aspects of the turbulence theory including the stochastic Navier-Stokes equation, stochastic Burgers equation and stochastic passive scalar and passive vector equations. Issues discussed include the existence of invariant measures, scaling of the structure functions, asymptotic behavior of the probability density f...
متن کامل0 Aspects of the stochastic Burgers equation and their connection with turbulence
Aspects of the stochastic Burgers equation and their connection with turbulence. Summary. We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless state to a structured state dominated by shocks. This transition takes...
متن کاملScaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential
The reordering of the multidimensional exponential quadratic operator in coordinatemomentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation...
متن کاملScaling and Exotic Regimes in Decaying Burgers Turbulence
We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time asymptotics. We exhibit new self-similar statistics of solutions describing phases with diluted shocks. Some speculations are included on the nature of systems w...
متن کاملOn stochastic differential equations and a generalised Burgers equation Dedicated to Professor Jia-an Yan on the Occasion of his 70th Birthday
In this paper, we discuss a link of Itô’s stochastic differential equations to nonlinear partial differential equations of Burgers type. Under certain conditions, we derive a generalised Burgers equation from a stochastic differential equation. We also give some economic interpretation of our result as well as the relevant conditions. Mathematics Subject Classification (2000): 60H10, 35K58, 91G99.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 46 شماره
صفحات -
تاریخ انتشار 2014