%0 Journal Article %1 menaldi2002stochastic %A Menaldi, Jose-Luis %A Sritharan, Sivaguru S. %D 2002 %J Applied Mathematics & Optimization %K 35q30-navier-stokes-equations 60h15-stochastic-analysis-pdes 76d05-incompressible-navier-stokes-equations 76m35-stochastic-analysis-applied-to-problems-in-fluid-mechanics %N 1 %P 31--30 %R 10.1007/s00245-002-0734-6 %T Stochastic 2-D Navier--Stokes Equation %U https://doi.org/10.1007/s00245-002-0734-6 %V 46 %X In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier--Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions--Prodi solutions to the deterministic Navier---Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier--Stokes martingale problem where the probability space is also obtained as a part of the solution.

@article{menaldi2002stochastic, abstract = {In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier--Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions--Prodi solutions to the deterministic Navier---Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier--Stokes martingale problem where the probability space is also obtained as a part of the solution.}, added-at = {2021-03-03T01:23:21.000+0100}, author = {Menaldi, Jose-Luis and Sritharan, Sivaguru S.}, biburl = {https://www.bibsonomy.org/bibtex/2928e73ccb24548ab01387bf01f81f370/gdmcbain}, day = 01, doi = {10.1007/s00245-002-0734-6}, interhash = {c2436a6153f74fd2625b5e4eef5937bc}, intrahash = {928e73ccb24548ab01387bf01f81f370}, issn = {1432-0606}, journal = {Applied Mathematics {\&} Optimization}, keywords = {35q30-navier-stokes-equations 60h15-stochastic-analysis-pdes 76d05-incompressible-navier-stokes-equations 76m35-stochastic-analysis-applied-to-problems-in-fluid-mechanics}, month = oct, number = 1, pages = {31--30}, timestamp = {2021-03-03T01:28:51.000+0100}, title = {Stochastic 2-D Navier--Stokes Equation }, url = {https://doi.org/10.1007/s00245-002-0734-6}, volume = 46, year = 2002 }