Local estimates and stability of viscous flows in an exterior domain

• Published in: Archive for rational mechanics and analysis Vol. 81; no. 4; pp. 333 - 347
• Main Authors: Galdi, G. P., Rionero, S.
• Format: Journal Article
• Language: English
• Published: 01-12-1983
• ISSN: 0003-9527; 1432-0673
• DOI: 10.1007/BF00250859

Continuous dependence upon the data and stability in the pointwise metric of solutions to the Navier-Stokes equations is proven in a class of motions which is larger than that considered by Cannon and Knightly (1970) and without appealing to any analyticity properties of solutions. After stating the problem of continuous dependence and stability, some lemmas concerning the weighted energy equality are proven along with a pointwise estimate for functions with bounded first derivatives in terms of their L(2) norm on compact sets. Some a priori estimates for solutions of the perturbed equations are given, and it is shown that, even if the velocity is allowed to grow polynomially at large spatial distances, the equation of motion forces it to be bounded and, in some cases, even to decay to zero. Continuous dependence theorems in the pointwise metric are obtained, and a stability theorem in the pointwise norm is proven.