A New Variational Approach to the Stability of Gravitational Systems |
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Authors: | Mohammed Lemou Florian Méhats Pierre Raphaël |
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Institution: | 1.CNRS and IRMAR, Université de Rennes 1,Rennes,France;2.IMT, Université Paul Sabatier,Toulouse,France |
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Abstract: | We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system
subject to its own gravity. A well-known conjecture in astrophysics is that the steady state solutions which are nonincreasing
functions of their microscopic energy are nonlinearly stable by the flow. This was proved at the linear level by several authors
based on the pioneering work by Antonov in 1961. Since then, standard variational techniques based on concentration compactness
methods as introduced by P.-L. Lions in 1983 have led to the nonlinear stability of subclasses of stationary solutions of
ground state type. |
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Keywords: | |
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