Mahir Hadžić

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Research

My research is in the field of mathematical analysis and nonlinear partial differential equations with an emphasis on mathematical problems associated with Euler equations, kinetic theory, and general relativity. Broadly speaking, my goal is to explore and rigorously describe possible dynamic scenarios arising from these equations. At the heart of it is the study of nonlinear stability of different phenomena, most notably questions of singularity formation and global stability of steady states. Due to the nonlinear character of the equations, such questions are in general hard and require the development of new techniques, often touching on other areas of mathematics (such as geometry, dynamical systems, and mathematical physics).

Much of my recent focus has been on compressible Euler equations, Newtonian self-gravitating systems describing star and galaxy evolution (the Euler-Poisson system and the Vlasov-Poisson system respectively), the relativistic self-gravitating systems (the Einstein-Euler system and the Einstein-Vlasov system), as well as the singularity formation for one of the classical free boundary problems - the Stefan problem. Please see my publications for more details.


Talks