L(2) stability for weak solutions of the NavierStokes equations in R(3)
Abstract
We consider the motion of a viscous fluid filling the whole space R3, governed by the classical NavierStokes equations (1). Existence of global (in time) regular solutions for that system of nonlinear 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.
 Publication:

Technical Summary Report Wisconsin Univ
 Pub Date:
 November 1985
 Bibcode:
 1985wisc.reptR....S
 Keywords:

 NavierStokes Equation;
 Solutions;
 Stability;
 Viscous Flow;
 Viscous Fluids;
 Differential Equations;
 Nonlinear Equations;
 Partial Differential Equations;
 Fluid Mechanics and Heat Transfer