A stochastic variational approach to viscous Burgers equations |
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Authors: | Ana Bela Cruzeiro Guo Ping Liu |
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Institution: | 1. GFMUL and Dep. de Matemática Instituto Superior Técnico(Universidade de Lisboa), Av. Rovisco Pais, 1049-001 Lisboa, Portugal;
2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, P. R. China |
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Abstract: | We consider viscous Burgers equations in one dimension of space and derive their solutions from stochastic variational principles on the corresponding group of homeomorphisms. The metrics considered on this group are L p metrics. The velocity corresponds to the drift of some stochastic Lagrangian processes. Existence of minima is proved in some cases by direct methods. We also give a representation of the solutions of viscous Burgers equations in terms of stochastic forward-backward systems. |
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Keywords: | Burgers equations stochastic variational principles Lagrangian diffusions |
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