Global well-posedness of 2D Navier–Stokes with Dirichlet boundary fractional noise
Antonio Agresti (TU Delft - Analysis)
Alexandra Blessing (Universität Konstanz)
Eliseo Luongo (Istituto Nanoscienze, Consiglio Nazionale delle Ricerche)
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Abstract
In this paper, we prove the global well-posedness and interior regularity for the 2D Navier-Stokes equations driven by a fractional noise acting as an inhomogeneous Dirichlet-type boundary condition. The model describes a vertical slice of the ocean with a relative motion between the two surfaces and can be thought of as a stochastic variant of the Couette flow. The relative motion of the surfaces is modeled by a Gaussian noise which is colored in space and fractional in time with Hurst parameter H > 3 4 .
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