This project is focussed on two basic areas in the field of nonlinear partial differential equations. First, the principal investigator aims to study the question of breakdown of three- dimensional incompressible and ideal fluid flow from the numerical and theoretical point of view. Second, he plans to investigate some regularity questions for the nonlinear Klein-Gordon equation: delayed singularity formation and global existence in low dimensions and breakdown of large amplitude solutions to three-dimensional semilinear equations. These studies will accrue to the foundations of applied areas such as aerodynamics, and wave propagation.
