The Annals of Probability

On the Stochastic Burgers’ Equation in the Real Line

István Gyöngy and David Nualart

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Abstract

In this paper we establish the existence and uniqueness of an $L^2(\mathbb{R})$ -valued solution for a one-dimensional Burgers’ equation perturbed by a space–time white noise on the real line. We show that the solution is continuous in space and time, provided the initial condition is continuous. The main ingredients of the proof are maximal inequalities for the stochastic convolution, and some a priori estimates for a class of deterministic parabolic equations.

Article information

Source
Ann. Probab., Volume 27, Number 2 (1999), 782-802.

Dates
First available in Project Euclid: 29 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022677386

Digital Object Identifier
doi:10.1214/aop/1022677386

Mathematical Reviews number (MathSciNet)
MR1698967

Zentralblatt MATH identifier
0939.60058

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60H20: Stochastic integral equations

Keywords
Stochastic Burgers’ equation space–time white noise

Citation

Gyöngy, István; Nualart, David. On the Stochastic Burgers’ Equation in the Real Line. Ann. Probab. 27 (1999), no. 2, 782--802. doi:10.1214/aop/1022677386. https://projecteuclid.org/euclid.aop/1022677386


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References

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