PARTIAL DIFFERENTIAL EQUATIONS, CALCULUS OF VARIATIONS, AND FLUID MECHANICS.
Abstract
The principal investigator completed six research papers during the period September 1967 through June 1968. This work is described in detail in the attached report. The major effort was devoted to nonlinear partial differential equations, the goal being to determine the effect of severe nonlinearity on the soluability of boundary value problems. A classification scheme into regularly elliptic and singularly elliptic equations was obtained by which one can directly determine the degree of nonlinearity of elliptic equations, and corresponding necessary and sufficient conditions of solvability were discovered. In fluid mechanics, the exact asymptotic relationship between Prandtl's boundary layer theory and the full Navier-Stokes equations was established for the case of flows in a radially convergent plane channel. Finally, two papers treated the existence and geometrical behavior of similarity solutions of the boundary layer equations, for free convection near a heated wall and for compressible flows past a boundary surface. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 18, 1968
- Accession Number
- AD0671488
Entities
People
- James B. Serrin
Organizations
- University of Minnesota