Colloquium: Roberto Camassa, University of North Carolina at Chapel Hill
Title: Hydrodynamic models and boundary confinement effects
Abstract: Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces with the confining boundaries. When contact happens, it can be shown that the model evolution can lead to the dependent variables developing singularities in finite time. The conditions and the nature of these singularities are illustrated in several cases, progressing from a single layer homogeneous fluid with a constant pressure free surface and flat bottom, to the case of a two-fluid system contained between two horizontal rigid plates, and finally, through numerical simulations, to the full Euler stratified system. These illustrate the qualitative and quantitative predictions of the models within a set of examples chosen to illustrate the theoretical results.
Bio: Roberto Camassa is Kenan Distinguished Professor in the Department
of Mathematics at the University of North Carolina at Chapel Hill.
He obtained his Ph.D. from the California Institute of Technology in
1990 with his primary adviser Ted Wu. Prof. Camassa is well-known
for inventing (together with Prof. Darryl Holm) of Camassa–Holm
Prof. Camassa's research interests include Nonlinear Evolution Equations,
Mathematical Modeling, Fluid Mechanics, and Optics. Together with
Prof. Rich McLaughlin, Prof. Camassa has built a state-of-the-art fluids
laboratory at UNC Chapel Hill, joint with the Department of Marine
Sciences, where numerous new phenomena in waves, turbulent mixing in
stratified fluids, and air-liquid pumping in lung airway geometries
have been discovered and explained mathematically.
Contact Name: Pavel Lushnikov