Seminar on Nonlinear Partial Differential Equations

When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations". A seminar was organized whose audience consisted of graduate students of the University and mature mathematicians who are not experts in the field. This volume contains 18 of these lectures. An effort is made to have an adequate Bibliography for further information. The Editor wishes to take this opportunity to thank all the speakers and the authors of the articles presented in this volume for their cooperation. S. S. Chern, Editor Table of Contents Geometrical and Analytical Questions Stuart S. Antman 1 in Nonlinear Elasticity An Introduction to Euler's Equations Alexandre J. Chorin 31 for an Incompressible Fluid Linearizing Flows and a Cohomology Phillip Griffiths 37 Interpretation of Lax Equations The Ricci Curvature Equation Richard Hamilton 47 A Walk Through Partial Differential Fritz John 73 Equations Remarks on Zero Viscosity Limit for Tosio Kato 85 Nonstationary Navier-Stokes Flows with Boundary Free Boundary Problems in Mechanics Joseph B. Keller 99 The Method of Partial Regularity as Robert V.

Geometrical and Analytical Questions in Nonlinear Elasticity.- An Introduction to Euler’s Equations for an Incompressible Fluid.- Linearizing Flows and a Cohomology Interpretation of Lax Equations.- The Ricci Curvature Equation.- A Walk Through Partial Differential Equations.- Remarks on Zero Viscosity Limit for Nonstationary Navier-Stokes Flows with Boundary.- Free Boundary Problems in Mechanics.- The Method of Partial Regularity as Applied to the Navier-Stokes Equations.- Shock Waves, Increase of Entropy and Loss of Information.- Stress and Riemannian Metrics in Nonlinear Elasticity.- The Cauchy Problem and Propagation of Singularities.- Analytical Theories of Vortex Motion.- The Minimal Surface Equation.- A Survey of Removable Singularities.- Applications of the Maximum Principle.- Minimax Methods and Their Application to Partial Differential Equations.- Analytic Aspects of the Harmonic Map Problem.- Equations of Plasma Physics.