Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions

Antonio Agresti; Eliseo Luongo

doi:10.1007/s00208-024-02812-0

Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions

Math Ann. 2024;390(2):2727-2766. doi: 10.1007/s00208-024-02812-0. Epub 2024 Feb 27.

Authors

Antonio Agresti^{1

2}, Eliseo Luongo³

Affiliations

¹ Institute of Science and Technology Austria (ISTA), Am Campus 1, 3400 Klosterneuburg, Austria.
² Present Address: Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.
³ Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy.

Abstract

The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier-Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured in space, can be interpreted as the physical law describing the driving mechanism on the atmosphere-ocean interface, i.e. as a balance of the shear stress of the ocean and the horizontal wind force.

Keywords: 60H15; 76D03 (47A60, 35J25).