STABLE SELF-SIMILAR BLOW UP DYNAMICS FOR THE THREE DIMENSIONAL RELATIVISTIC GRAVITATIONAL VLASOV-POISSON SYSTEM

摘要

Setting of the problem. Consider the N dimensional gravitational Vlasov-Poisson system, with N = 3 or 4: where we denoted for a given distribution function f ≥ 0: and σN is the area of the unit sphere in RN (σ3 = 4π and σ4 = 2π2). This nonlinear transport equation describes in dimension N = 3 the mechanical state of a stellar system subject to its own gravity (see for instance [3, 14]).