L(2) Stability for Weak Solutions of the Navier-Stokes Equations in R(3).
Abstract
We consider the motion of a viscous fluid filling the whole space R3, governed by the classical Navier-Stokes equations (1). Existence of global (in time) regular solutions for that system of non-linear partial differential equations is still an open problem. Up to now, the only available global existence theorem (other than for sufficiently small initial data) is that of weak (turbulent) solutions. From both the mathematical and the physical point of view, an interesting property is the stability of such weak solutions. We assume that v(t,x) is a solution, with initial datum vO(x). We suppose that the initial datum is perturbed and consider one weak solution u corresponding to the new initial velocity. Then we prove that, due to viscosity, the perturbed weak solution u approaches in a suitable norm the unperturbed one, as time goes to + infinity, without smallness assumptions on the initial perturbation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1985
- Accession Number
- ADA163612
Entities
People
- Paolo Secchi
Organizations
- University of Wisconsin–Madison