 05391 Juerg Froehlich and Enno Lenzmann
 BlowUp for Nonlinear Wave Equations describing Boson Stars
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Nov 14, 05

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Abstract. We consider the nonlinear wave equation $i \partial_t u= \sqrt{\Delta + m^2} u  (x^{1} \ast u^2) u$ on $\RR^3$ modelling the dynamics of (pseudorelativistic) boson stars. For spherically symmetric initial data, $u_0(x) \in C^\infty_{c}(\RR^3)$, with negative energy, we prove blowup of $u(t,x)$ in $H^{1/2}$norm within a finite time. Physically, this phenomenon describes the onset of "gravitational collapse" of a boson star. We also study blowup in external, spherically symmetric potentials and we consider more general Hartreetype nonlinearities. As an application, we exhibit instability for ground state solitary waves of the equation with $m=0$.
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