The asymptotic stability of the generalized 3D Navier-Stokes equations
Summary: We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solution \(u\) of the Navier-Stokes equations lies in the regular class \(\nabla u\in L^p(0,\infty;B^0_{q,\infty}(\mathbb R^3))\), \((2\alpha/p)+(3/q)=2\alpha\), \(2<q<\infty\), \(0<\alpha<1\), then every weak solution \(v(x,t)\) of the perturbed system converges asymptotically to \(u(x,t)\) as \(\| v(t)-u(t)\|_{L^2}\to 0\), \(t\to\infty\).
scientific article; zbMATH DE number 6950617