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Local estimates and stability of viscous flows in an exterior domain. (English) Zbl 0544.76028
The authors prove the pointwise continuous dependence of solutions of the incompressible Navier-Stokes equations on the boundary and initial data as well as the pointwise stability of solutions with respect to perturbations whose growth at large distances is appropriately restricted. Previous results on these problems assume analyticity of both the solution and the perturbation, but the present paper makes no appeal to analyticity. Instead the authors use various inequalities in weighted \(L^ p\)-spaces to estimate the perturbed velocity field and its gradients and thereby derive pointwise estimates that imply continuous dependence and stability.
Reviewer: F.Howes

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76E30 Nonlinear effects in hydrodynamic stability
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35Q30 Navier-Stokes equations
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