Zobrazeno 1 - 10
of 139
pro vyhledávání: '"Luk, Jonathan"'
Autor:
Huneau, Cécile, Luk, Jonathan
We review recent mathematical results concerning the high-frequency solutions to the Einstein vacuum equations and the limits of these solutions. In particular, we focus on two conjectures of Burnett, which attempt to give an exact characterization o
Externí odkaz:
http://arxiv.org/abs/2404.07659
Autor:
Luk, Jonathan, Oh, Sung-Jin
We introduce a general method for understanding the late time tail for solutions to wave equations on asymptotically flat spacetimes with odd space dimensions. In particular, for a large class of equations, we prove that the precise late time tail is
Externí odkaz:
http://arxiv.org/abs/2404.02220
Autor:
Huneau, Cécile, Luk, Jonathan
We prove Burnett's conjecture in general relativity when the metrics satisfy a generalized wave coordinate condition, i.e., suppose $\{g_n\}_{n=1}^\infty$ is a sequence of Lorentzian metrics (in arbitrary dimensions $d \geq 3$) satisfying a generaliz
Externí odkaz:
http://arxiv.org/abs/2403.03470
Autor:
Luk, Jonathan, Moschidis, Georgios
The emergence of trapped surfaces in solutions to the Einstein field equations is intimately tied to the well-posedness properties of the corresponding Cauchy problem in the low regularity regime. In this paper, we study the question of existence of
Externí odkaz:
http://arxiv.org/abs/2204.09855
Motivated by the strong cosmic censorship conjecture, we study the linear scalar wave equation in the interior of subextremal strictly charged Reissner-Nordstr\"om black holes by analyzing a suitably-defined "scattering map" at $0$ frequency. The met
Externí odkaz:
http://arxiv.org/abs/2201.12294
Autor:
Chaturvedi, Sanchit, Luk, Jonathan
Consider the linear transport equation in $1$D under an external confining potential $\Phi$: \begin{equation*} \partial_t f + v \partial_x f - \partial_x \Phi \partial_v f = 0. \end{equation*} For $\Phi = \frac{x^2}{2} + \frac{\epsilon x^4}{2}$ (with
Externí odkaz:
http://arxiv.org/abs/2109.12402
Autor:
Luk, Jonathan, Oh, Sung-Jin
We extend the monumental result of Christodoulou-Klainerman on the global nonlinear stability of the Minkowski spacetime to the global nonlinear stability of a class of large dispersive spacetimes. More precisely, we show that any regular future caus
Externí odkaz:
http://arxiv.org/abs/2108.13379
Autor:
Luk, Jonathan, Speck, Jared
Publikováno v:
Analysis & PDE 17 (2024) 831-941
Consider a $1$D simple small-amplitude solution $(\rho_{(bkg)}, v^1_{(bkg)})$ to the isentropic compressible Euler equations which has smooth initial data, coincides with a constant state outside a compact set, and forms a shock in finite time. Viewi
Externí odkaz:
http://arxiv.org/abs/2107.03426
Autor:
Luk, Jonathan, Van de Moortel, Maxime
This is the second and last paper of a series aimed at solving the local Cauchy problem for polarized $\mathbb U(1)$ symmetric solutions to the Einstein vacuum equations featuring the nonlinear interaction of three small amplitude impulsive gravitati
Externí odkaz:
http://arxiv.org/abs/2106.05479
Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu Q(F,F)(t,x,v),\\ E(t,x
Externí odkaz:
http://arxiv.org/abs/2104.05692