Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Arick Shao"'
Autor:
Athanasios Chatzikaleas, Arick Shao
We reconsider the unique continuation property for a general class of tensorial Klein-Gordon equations of the form \begin{align*} \Box_{g} \phi + \sigma \phi = \mathcal{G}(\phi,\nabla \phi) \text{,} \qquad \sigma \in \mathbb{R} \end{align*} on a larg
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7eaeb962185cdf65678948febe0b8fe6
http://arxiv.org/abs/2201.06010
http://arxiv.org/abs/2201.06010
Autor:
Gustav Holzegel, Arick Shao
In this paper, we consider vacuum asymptotically anti-de Sitter spacetimes $( \mathscr{M}, g )$ with conformal boundary $( \mathscr{I}, \mathfrak{g} )$. We establish a correspondence, near $\mathscr{I}$, between such spacetimes and their conformal bo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30632dd1f0524d0cbb65062d1b54bc3e
Autor:
Arick Shao
Publikováno v:
Séminaire Laurent Schwartz — EDP et applications. :1-14
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::48a04dce89bb37cffabda73c1ebaa060
https://doi.org/10.5802/slsedp.134
https://doi.org/10.5802/slsedp.134
Autor:
Arick Shao, Alex McGill
We consider the question of whether solutions of Klein--Gordon equations on asymptotically Anti-de Sitter spacetimes can be uniquely continued from the conformal boundary. Positive answers were first given by the second author with G. Holzegel, under
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::399b0cd9705388060157cdef91cfe9be
http://arxiv.org/abs/2008.07416
http://arxiv.org/abs/2008.07416
Autor:
Arick Shao, Spyros Alexakis
Publikováno v:
Transactions of the American Mathematical Society. 369:5525-5542
We consider singularities of the focusing subconformal nonlinear wave equation and some generalizations of it. At noncharacteristic points on the singularity surface, Merle and Zaag have identified the rate of blow-up of the $H^1$-norm of the solutio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::67140336c553da6499fe9d7e2cbf977f
https://doi.org/10.1090/tran/6820
https://doi.org/10.1090/tran/6820
Publikováno v:
Advances in Mathematics. 286:481-544
We prove various uniqueness results from null infinity, for linear waves on asymptotically flat space-times. Assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities, we derive that the solution must v
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2050aa772dd34ccf894d6566d67fe168
https://doi.org/10.1016/j.aim.2015.08.028
https://doi.org/10.1016/j.aim.2015.08.028
Autor:
Spyros Alexakis, Arick Shao
Publikováno v:
Journal of the European Mathematical Society. 18:2045-2106
We consider smooth null cones in a vacuum spacetime that extend to future null infinity. For such cones that are perturbations of shear-free outgoing null cones in Schwarzschild spacetimes, we prove bounds for the Bondi energy, momentum, and rate of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::156b6f2c8f022b1a9a68acbb811a7b5b
https://doi.org/10.4171/jems/638
https://doi.org/10.4171/jems/638
Autor:
Arick Shao
Publikováno v:
Classical and Quantum Gravity. 38:034001
We study the geometry of a general class of vacuum asymptotically Anti-de Sitter spacetimes near the conformal boundary. In particular, the spacetime is only assumed to have finite regularity, and it is allowed to have arbitrary boundary topology and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::de6f51abc647560347d920e65ad5434d
https://doi.org/10.1088/1361-6382/abc81a
https://doi.org/10.1088/1361-6382/abc81a
Autor:
Arick Shao
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a fully general
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94bd11070347c83680c201882079e44e
Autor:
Arick Shao, Spyros Alexakis
Publikováno v:
Journal of Functional Analysis. 269:3458-3499
We prove a unique continuation from infinity theorem for regular waves of the form $[ \Box + \mathcal{V} (t, x) ]\phi=0$. Under the assumption of no incoming and no outgoing radiation on specific halves of past and future null infinities, we show tha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d658a8e32419848acdb587011f81b98
https://doi.org/10.1016/j.jfa.2015.08.012
https://doi.org/10.1016/j.jfa.2015.08.012