Abstract
We show that the incompressible 3D Navier–Stokes system in a \({{\mathscr{C}}^{1,1}}\) bounded domain or a bounded convex domain \({\Omega}\) with a non penetration condition \({\nu\cdot u=0}\) at the boundary \({\partial\Omega}\) together with a time-dependent Robin boundary condition of the type \({\nu\times{\rm curl}\,u=\beta(t) u}\) on \({\partial\Omega}\) admits a solution with enough regularity provided the initial condition is small enough in an appropriate functional space.
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Communicated by M. Hieber
The research of both authors was partially supported by the ANR Project HAB, ANR-12-BS01-0013-02 and ANR-12-BS01-0013-03.
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Monniaux, S., Ouhabaz, E.M. The Incompressible Navier–Stokes System with Time-Dependent Robin-Type Boundary Conditions. J. Math. Fluid Mech. 17, 707–722 (2015). https://doi.org/10.1007/s00021-015-0227-4
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DOI: https://doi.org/10.1007/s00021-015-0227-4