Borel Summation and Applications to PDEs

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

The project focuses on further development of new and constructive techniques for proving existence of solutions to nonlinear partial differential equations, with special emphasis on the three-dimensional Navier-Stokes system, and determining their global and asymptotic properties. The methods are based on recent advances in Borel-Laplace regularization and summability. Nonlinear partial differential equations are essential modeling tools in a wide range of problems in physics, chemistry, biology and other sciences. Understanding their solutions is a key tool in interpreting and predicting physical phenomena. The project develops a new approach and methods for this scientific enterprise.