Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

CSIC Building (#406), Seminar Room 4122.
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Spatial complexity of solutions of partial differential equations

Dr. Igor Kukavica

Mathematics at University of S California

Abstract:   We address spatial complexity of solutions of the Kuramoto-Sivashinsky equation. We show that for any solution $u$ on the global attractor, the following holds: For any number $p$, the number of zeros of $u-p$ can be bounded by a quantity which depends polynomially on the spatial period. We will also discuss dependence of the bounds on parameters of the equation.