Almost sure existence of global weak solutions for incompressible generalized Navier-Stokes equations

2025/02/21 by Lin, Yuan-Xin, Wang, Ya-Guang · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.15273

Abstract

In this paper we consider the initial value problem of the incompressible generalized Navier-Stokes equations in torus \mathbbT^d with d ≥ 2. The generalized Navier-Stokes equations is obtained by replacing the standard Laplacian in the classical Navier-Stokes equations by the fractional order Laplacian -(-Δ)^\al with \al ∈ ( (2)/(3),1 ]. After an appropriate randomization on the initial data, we obtain the almost sure existence of global weak solutions for initial data being in \DotH^s(\mathbbT^d) with s∈ (1-2\al,0).

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• Almost sure global weak solutions and optimal decay for the incompressible generalized Navier-Stokes equations

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