The martingale problem associated to the three-dimensional Navier–Stokes equations is shown to have a family of solutions satisfying the Markov property. The result is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times, thus showing that every Markov selection has a property of continuous dependence on initial conditions.
Il est établi que le problème de martingales associé aux équations de Navier–Stokes tridimensionnelles possède une famille de solutions qui satisfont la propriété de Markov. Ce résultat est obtenu par un principe abstrait de sélection. La propriété de Markov est fondamentale pour étendre la régularité du semi groupe de transition des petites échelles de temps à des échelles arbitraires, en établissant en particulier que chaque sélection de Markov dépend continûment des conditions initiales.
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Franco Flandoli 1; Marco Romito 2
@article{CRMATH_2006__343_1_47_0, author = {Franco Flandoli and Marco Romito}, title = {Markov selections and their regularity for the three-dimensional stochastic {Navier{\textendash}Stokes} equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {47--50}, publisher = {Elsevier}, volume = {343}, number = {1}, year = {2006}, doi = {10.1016/j.crma.2006.04.025}, language = {en}, }
TY - JOUR AU - Franco Flandoli AU - Marco Romito TI - Markov selections and their regularity for the three-dimensional stochastic Navier–Stokes equations JO - Comptes Rendus. Mathématique PY - 2006 SP - 47 EP - 50 VL - 343 IS - 1 PB - Elsevier DO - 10.1016/j.crma.2006.04.025 LA - en ID - CRMATH_2006__343_1_47_0 ER -
Franco Flandoli; Marco Romito. Markov selections and their regularity for the three-dimensional stochastic Navier–Stokes equations. Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 47-50. doi : 10.1016/j.crma.2006.04.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.025/
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