Friday, April 21 at 2:00pm to 3:00pm
Kaprielian Hall (KAP), 414
3620 South Vermont Avenue, Los Angeles, CA 90089
Allen Yilun Wu, Brown University
The equilibrium shape and density distribution of rotating fluid under self-gravitation is a classical problem in mathematical physics. Early efforts beginning in the eighteenth century were devoted to finding ellipsoidal shapes with constant density. In the twentieth century, major progress was made by studying steady rotating solutions to the compressible Euler-Poisson equations. Two methods of constructing solutions have been used. Assuming a polytropic equation of state $p=\rho^\gamma$, a variational method, pioneered by the work of Auchmuty and Beals, proves existence of solutions if $\gamma>\frac43$. On the other hand, we present a perturbative result that establishes existence for $\gamma>\frac65$. The method is built upon an old work of Lichtenstein. We also prove an analogous result for the Vlasov-Poisson equations modeling a similar physical problem.