Global well-posedness of 2D Navier-Stokes with Dirichlet boundary fractional noise

2024/07/04 by Agresti, Antonio, Blessing, Alexandra, Luongo, Eliseo · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.03988

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 coloured in space and fractional in time with Hurst parameter greater than 3/4.

Cited by

• Global well-posedness for small data in a 3D temperature-velocity model with Dirichlet boundary noise

Related

• Global well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions
• Global well-posedness for 2D fractional inhomogeneous Navier-Stokes equations with rough density
• Strong well-posedness of the two-dimensional stochastic Navier-Stokes equation on moving domains
• Navier-Stokes Equations with Navier Boundary Conditions and Stochastic Lie Transport: Well-Posedness and Inviscid Limit
• Well-posedness and regularity for the fractional Navier-Stokes equations