<Emphasis Type="Italic">m</Emphasis>-Dissipativity of Kolmogorov Operators Corresponding to Burgers Equations with Space-time White Noise |
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Authors: | Giuseppe Da Prato Arnaud Debussche |
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Institution: | (1) Scuola Normale Superiore, 56126 Pisa, Italy;(2) Ecole Normale Supérieure de Cachan, antenne de Bretagne, Campus de Ker Lann, 35170 Bruz, France |
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Abstract: | In this article, we prove new a priori estimates on the solutions of the Burgers equation driven by a space-time white noise and on the associated invariant measure.
We also prove smoothing properties for the transition semi-group. This is obtained thanks to the introduction of a modified
Kolmogorov operator. These results are then used to prove that the Kolmogorov operator associated to the Burgers equation
is m-dissipative. This implies several properties on the Kolmogorov equation.
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Keywords: | stochastic Burgers equation finiteness of moments smoothing properties Kolmogorov equation m-dissipativity identité du carré du champ |
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