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On the Stochastic Burgers’ Equation in the Real Line

Gyöngy, István
; 
Nualart, David
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Abstract
In this paper we establish the existence and uniqueness of an L2(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.
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This is the publisher's version, also available electronically from http://projecteuclid.org/euclid.aop/1022677386#abstract.
Date
1999-01-01
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Institute of Mathematical Statistics
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Mathematics Scholarly Works
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NualartD_AoP_27(2)782.pdf
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Gyöngy, István; Nualart, David. On the Stochastic Burgers’ Equation in the Real Line. Ann. Probab. 27 (1999), no. 2, 782--802. www.dx.doi.org/10.1214/aop/1022677386.
URI
https://hdl.handle.net/1808/17392
DOI
10.1214/aop/1022677386
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