### Alcune questioni matematiche riguardanti la dinamica stellare

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According to general relativity, a binary consisting of spinning bodies will precess due to spin-orbit and spin-spin coupling. The corresponding modulation of its gravitational waves might be a serious problem for detecting such waves with simple post-Newtonian templates. A new family of templates that takes into account the complications arising from the orbital precession is proposed and its application and performance are discussed.

In this work, we prove the nonlinear stability of galaxy models derived from the three dimensional gravitational Vlasov Poisson system, which is a canonical model in astrophysics to describe the dynamics of galactic clusters.

The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that $u\in {W}_{r}^{2,1}\left({\tilde{\Omega}}^{T}\right)$ with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the ${L}_{p}$-approach the Lagrangian coordinates must be used. We are looking...

A priori estimates for solutions of a system describing the interaction of gravitationally attracting particles with a self-similar pressure term are proved. The presented theory covers the case of the model with diffusions that obey either Fermi-Dirac statistics or a polytropic one.

We give a review of results on the initial value problem for the Vlasov--Poisson system, concentrating on the main ingredients in the proof of global existence of classical solutions.

We review the main results concerning the global existence and the stability of solutions for some models of viscous compressible self-gravitating fluids used in classical astrophysics.