Existence of Solutions to the Nonhomogeneous Steady Navier-Stokes Equations.
Abstract
This paper concerns the existence of steady solutions to the Navier-Stokes equations in a bounded domain. The condition of solenoidality for the velocity field imposes a necessary condition on the boundary data. For a certain class of symmetrical domains, the authors show that this necessary condition implies the existence of a solution to the problem. The method consists of proving a priori bounds on solutions by assuming the contrary, rescaling the equations, and then arriving at a solution to the steady Euler equations in the limit. Examination of this equation leads to the desired contradiction. After one has suitable bounds on any solutions, one uses the Leray-Schauder theorem to prove existence. In addition, the authors remark on the problem of a general bounded domain, and suggest how certain maximum principles might yield the expected results.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1983
- Accession Number
- ADA129171
Entities
People
- Charles J. Amick
Organizations
- University of Wisconsin–Madison