Stochastic Burgers’ equation. (English) Zbl 0824.35112

The authors prove that the stochastic Burger’s equation forced by a cylindrical Wiener process with Dirichlet boundary conditions and the initial condition has a unique global solution. Also the existence of an invariant measure for the corresponding transition semigroup is established.


35Q53 KdV equations (Korteweg-de Vries equations)
35R60 PDEs with randomness, stochastic partial differential equations
Full Text: DOI


[1] D. H. CHAMBERS, R. J. ADRIAN, P. MOIN, D. S. STEWART, H. J. SUNG, Karhunen-Loéve expansion of Burgers’ model of turbulence,Phys. Fluids 31, (9), 2573-2582 (1988)
[2] H. CHOI, R. TEMAM, P. MOIN, J. KIM, Feedback control for unsteady flow and its application to Burgers equation, Center for Turbulence Research, Stanford University, CTR Manuscript 131. To appear on J. Fluid Mechanics (1992) · Zbl 0810.76012
[3] H. CRAUEL, F. FLANDOLI, Attractors for Random Dynamical Systems, Preprint n. 148 Scuola Normale Superiore di Pisa (1992) · Zbl 0819.58023
[4] DAH-TENG JENG Forced Model Equation for Turbulence,The Physics of Fluids 12, 10, 2006-2010 (1969) · Zbl 0187.51604
[5] F. FLANDOLI, Dissipativity and invariant measures for stochastic Navier-Stokes equations Preprint n. 24 Scuola Normale Superiore di Pisa (1993)
[6] I. HOSOKAWA, K. YAMAMOTO, Turbolence in the randomly forced one dimensional Burgers flow,J. Stat. Phys. 13, 245 (1975)
[7] M. KARDAR, M. PARISI, J. C. ZHANG Dynamical scaling of growing interfaces,Phys. Rev. Lett. 56, 889 (1986) · Zbl 1101.82329
[8] G. DA PRATO, J. ZABCZYK, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications, Cambridge University Press (1992) · Zbl 0761.60052
[9] F. ROTHE (1984), Global Solutions of Reaction-Diffusion Systems,Lecture Notes in Mathematics,1072, Springer-Verlag (1984) · Zbl 0546.35003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.