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On the strong solution for the 3D stochastic Leray-\(\alpha\) model. (English) Zbl 1187.35011
Summary: We prove the existence and uniqueness of strong solution to the stochastic Leray-\(\alpha \) equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation scheme. We also study the asymptotic behaviour of the strong solution as alpha goes to zero. We show that a sequence of strong solutions converges in appropriate topologies to weak solutions of the 3D stochastic Navier-Stokes equations.

MSC:
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35D35 Strong solutions to PDEs
35R60 PDEs with randomness, stochastic partial differential equations
35Q30 Navier-Stokes equations
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References:
[1] doi:10.1098/rspa.2004.1373 · Zbl 1145.76386 · doi:10.1098/rspa.2004.1373
[2] doi:10.1016/j.jmaa.2004.12.048 · Zbl 1081.35083 · doi:10.1016/j.jmaa.2004.12.048
[5] doi:10.1007/BF00996149 · Zbl 0836.35115 · doi:10.1007/BF00996149
[6] doi:10.1155/2009/723236 · Zbl 1417.76015 · doi:10.1155/2009/723236
[9] doi:10.1155/S1048953300000228 · Zbl 0974.60045 · doi:10.1155/S1048953300000228
[10] doi:10.1098/rspa.2005.1574 · Zbl 1149.35397 · doi:10.1098/rspa.2005.1574
[13] doi:10.1214/aop/1015345773 · Zbl 1032.60055 · doi:10.1214/aop/1015345773
[14] doi:10.3792/pjaa.81.89 · Zbl 1330.35554 · doi:10.3792/pjaa.81.89
[18] doi:10.1007/s00245-003-0773-7 · Zbl 1049.60058 · doi:10.1007/s00245-003-0773-7
[20] doi:10.1137/1135082 · Zbl 0735.60061 · doi:10.1137/1135082
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