On the Approximation of the Stochastic Burgers Equation |
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Authors: | Christoph Gugg Hansjörg Kielhöfer Michael Niggemann |
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Institution: | Institut für Mathematik, Universit?t Augsburg, 86135 Augsburg, Germany; E-mail:Kielhoefer@math.uni-augsburg.de, DE Fachhochschule Würzburg-Schweinfurt, 97070 Würzburg, Germany;, DE
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Abstract: | We prove mathematical approximation results for the (hyperviscous) Burgers equation driven by additive Gaussian noise. In
particular we show that solutions of ``approximating equations' driven by a discretized noise converge towards the solution
of the original equation when the discretization parameter gets small. The convergence takes place in the expected value of
arbitrary powers of certain norms; i.e., all moments of the difference of the solutions tend to zero in certain function spaces.
For the hyperviscous Burgers equation, these results are applied to justify the approximation of certain correlation functions
that play a major role in statistical turbulence theory.
Received: 10 October 2001 / Accepted: 21 May 2002 Published online: 6 August 2002 |
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