Name	Morimichi Umehara
	Department	Department of Mathematics, School of Fundamental Science and Technology
	Research Fields	Partial Differential Equations/Fluid Mechanics

Mathematical Analyses of Equations for a Compressible Viscous Gaseous Star

 It is said that stars originate in processes of gathering many gaseous particles under their self-gravitations, and when we observe the universe in the more macroscopic scale, stars are gathered again by their own self-gravitations, and constructing the large-scale structure of the universe: galaxies, galactic systems, etc. In analyzing these structures which have different space scales, their motions are uniformly described by hydrodynamical equations as corresponding initial-boundary value problems.

 Currently I study the free-boundary problems for both the one-dimensional and the three-dimensional spherically symmetric models taking into account influences of the self-gravitation, the radiation and the reacting processes. Until now, as concerns the problems of gaseous stars mentioned above, since mathematical results for the model equations taking into account physically suitable assumptions are not obtained sufficiently, I aim to construct the mathematical theory for the models describing physically the more valid and rich phenomena.