The investigator carries out a qualitative study of partial differential equations arising as models in fluid mechanics and chemistry. Understanding the properties of these models is a fundamental challenge both in mathematics and science. The regularity and stability of solutions are issues strongly related to nontrivial physical phenomena like turbulence and phase transitions that are complex multiscale problems. Analyzing mathematical models of these phenomena often requires the development of novel tools encompassing techniques from analysis, applied mathematics, and stochastics. This project, which addresses both theoretical and applied issues, spans from conservation laws to Navier-Stokes equations, kinetic equations, and motion of particles in fluids. It requires tools from the theories of nonlinear partial differential equations, asymptotic analysis, probability, and stochastics.
The discovery of mathematical structure in physical models is of great importance for a deeper understanding of the physical phenomena themselves. It gives also some hints of the range of validity of the models. In this project, the investigator develops and studies new models involving couplings between fluid mechanics and physics far from equilibrium. This field has important applications in science and engineering. For example, it models pollutants in a river or combustion of gasoline in an engine. The applied and mathematical challenges stem from the complexity of the phenomena.
