Nonlinear Partial Differential Equation

Gravitational Collapse of Self-similar stars

-

B1 L4 R4102

The Euler-Poisson equations give the classical model of a self-gravitating star under Newtonian gravity. It is widely expected that, in certain regimes, initially smooth initial data may give rise to blow-up solutions, corresponding to the collapse of a star under its own gravity. In this talk, I will present recent work with Yan Guo, Mahir Hadzic and Juhi Jang that demonstrates the existence of smooth, radially symmetric, self-similar blow-up solutions for this problem. I will also comment on the stability of the obtained solution. At the heart of the analysis is the presence of a sonic point, a singularity in the self-similar model that poses serious analytical challenges in the search for a smooth solution.

Simone Portaro

Simone Portaro is a Ph.D. Student in the Computer, Electrical, Mathematical Sciences and Engineering (CEMSE) department at the Applied Mathematics and Computational Sciences (AMCS) program under the supervision of Professor Peter Markowich at King Abdullah University of Science and Technology. Simone received his B.S. degree in Industrial Engineering from the University of Catania, Italy in 2017. In 2020, he received his M.S. degree in Mathematical Engineering from Politecnico di Torino, Italy. Research interests Nonlinear Partial Differential Equations, Analysis-Modeling of biological network

Shuaikun Wang

Short Bio Shuaikun Wang received his bachelor's degree in Mathematics from University of Science and Technology of China in 2012 and a Ph.D degree in Mathematics from City University of Hong Kong in 2016. He was a postdoc in City University of Hong Kong in 2016-2017 and a Postdoctoral Research Fellow in the Applied PDE group at KAUST from September 2017 - December 2020. Currently he is an Associate Professor in the School of Mathematics, Shandong University, Jinan, China. Shuaikun Wang's research interests lie in the area of applied analysis, nonlinear partial differential equations and