Abstract
AbstractThe 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.
Funder
H2020 European Research Council
Scuola Normale Superiore
Publisher
Springer Science and Business Media LLC
Reference54 articles.
1. Agresti, A., Hussein, A.: Maximal $$L^p$$-regularity and $$H^\infty $$-calculus for block operator matrices and applications. J. Funct. Anal. 285(11), 110146 (2023)
2. Agresti, A., Veraar, M.: Stability properties of stochastic maximal $${L}^p$$-regularity. J. Math. Anal. Appl. 482(2), 123553 (2020)
3. Agresti, A., Lindemulder, N., Veraar, M.: On the trace embedding and its applications to evolution equations. Math. Nachr. 296(4), 1319–1350 (2023)
4. Alòs, E., Bonaccorsi, S.: Stochastic partial differential equations with Dirichlet white-noise boundary conditions. Ann. l’IHP Probab. Stat. 38(2), 125–154 (2002)
5. Amann, H.: Linear and Quasilinear Parabolic Problems, vol. 1. Springer, New York (1995)