Abstract
Weak solutions to the Stokes and Navier-Stokes problems are proved to exist in domains which, outside a ball, coincide with the three-dimensional layer ℝ2 × (0,1). Apart from solutions with the finite Dirichlet integral, solutions to the linear problem are constructed with a prescribed behavior at infinity such that the plane-parallel Poiseuille and Couette flows, the rotational flow. A solution to the nonlinear problem is found that drives a nonzero flux to infinity and becomes unique under the data smallness assumption. Estimates for weighted norms of the pressure are derived as well
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Accepted: August 28, 1998
Rights and permissions
About this article
Cite this article
Nazarov, S., Pileckas, K. On the Solvability of the Stokes and Navier-Stokes Problems in the Domains That Are Layer-Like at Infinity. J. math. fluid mech. 1, 78–116 (1999). https://doi.org/10.1007/s000210050005
Published:
Issue Date:
DOI: https://doi.org/10.1007/s000210050005