Matthew R. I. Schrecker

Research

My primary research is in the field of non-linear partial differential equations (PDE) with an emphasis on those equations arising in the study of gas dynamics. Much of my research so far has been on the Euler equations of fluid mechanics, a fundamental system of PDE at the interface of mathematical analysis, mathematical physics and engineering. Due to the formation of shock waves (discontinuities in the flow), the Euler equations are a highly complex system of equations that pose significant challenges to mathematical analysis. I have mostly been working in three areas under this broad heading: the existence of admissible weak solutions under the assumption of finite energy; the shock reflection problem; and the problem of singularity formation for the gravitational Euler-Poisson system, a simple model for stellar collapse. These problems require the development and application of a range of techniques in analysis and PDE theory, often touching other areas of mathematics such as differential geometry and mathematical physics.

Please see my publications for more details.