arXiv subjects

Yannis Angelopoulos

Publications and source records attributed to Yannis Angelopoulos.

22 records · Page 2Linked to original sources

arXiv2018

A vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary spacetimes

We present a new vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes. Specifically, we derive a new hierarchy of higher-order weighted energy estimates by employing appropriate commutator vector fields. In cases where an integrated local energy decay estimate holds, like in the case of sub-extremal Reissner-Nordstrom black holes, this hierarchy leads to almost-sharp global energy and pointwise time-decay estimates with decay rates that go beyond those obtained by the traditional vector field method. Our estimates play a fundamental role in our companion paper where precise late-time asymptotics are obtained for linear scalar fields on such backgrounds.

math.AP↗

arXiv2018

Late-time asymptotics for the wave equation on spherically symmetric, stationary spacetimes

We derive precise late-time asymptotics for solutions to the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes including as special cases the Schwarzschild and Reissner-Nordstrom families of black holes. We also obtain late-time asymptotics for the time derivatives of all orders and for the radiation field along null infinity. We show that the leading-order term in the asymptotic expansion is related to the existence of the conserved Newman-Penrose quantities on null infinity. As a corollary we obtain a characterization of all solutions which satisfy Price's polynomial law as a lower bound. Our analysis relies on physical space techniques and uses the vector field approach for almost-sharp decay estimates introduced in our companion paper. In the black hole case, our estimates hold in the domain of outer communications up to and including the event horizon. Our work is motivated by the stability problem for black hole exteriors and strong cosmic censorship for black hole interiors.

math.AP↗

arXiv2014

Nonlinear Wave Equations With Null Condition On Extremal Reissner-Nordström Spacetimes I: Spherical Symmetry

We study spherically symmetric solutions of semilinear wave equations in the case where the nonlinearity satisfies the null condition on extremal Reissner--Nordstrom black hole spacetimes. We show that solutions which arise from sufficiently small compactly supported smooth data prescribed on a Cauchy hypersfurace \widetilde{Σ}_0 crossing the future event horizon \mathcal{H}^{+} are globally well-posed in the domain of outer communications up to and including \mathcal{H}^{+}. Our method allows us to close all bootstrap estimates under very weak decay results (compatible with those known for the linear case). Moreover we establish a certain number of non-decay and blow-up results along the horizon \mathcal{H}^{+} which generalize known instability results for the linear case. Our results apply to spherically symmetric wave maps for a wide class of target spaces.

math.AP↗

arXiv2013

Well-posedness and ill-posedness results for the Novikov-Veselov equation

In this paper we study the Novikov-Veselov equation and the related modified Novikov-Veselov equation in certain Sobolev spaces. We prove local well-posedness in H^s (R2) for s > 1/2 for the Novikov-Veselov equation, and local well-posedness in H^s (R2) for s > 1 for the modified Novikov-Veselov equation. Finally we point out some ill-posedness issues for the Novikov- Veselov equation in the supercritical regime.

math.AP↗