A Pregenerator for Burgers Equation¶Forced by Conservative Noise
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We consider the stationarity of a Burgers equation with an external random force of gradient type in one space dimension. The expected stationary measure is the white noise measure on the space of tempered distributions. As a consequence, the nonlinearity of the formal equation u t +λu u x =νu xx +η x is ill-defined. Introducing a pregenerator we can formulate a generalized martingale problem leading to a meaningful version of the formal equation which was an open problem.
KeywordsWhite Noise Open Problem Stationary Measure Noise Measure Space Dimension
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