11 citations · 31 across the 11 of their papers we have counts for
11 papers
Two global stability theorems for small-data compressible Euler solutions: Unique maximal globally hyperbolic developments with gradient-blowup & smooth global existence in the entire spacetime
Leonardo Abbrescia, Jared Speck, Dongxiao Yu
We prove a pair of complementary small-data stability theorems describing the global future and past structure of classical solutions to the isentropic, spherically symmetric …
The emergence of the Cauchy horizon from the crease for compressible Euler flow
Leonardo Abbrescia, Jared Speck
We study open sets of nearly plane symmetric data for the compressible Euler equations with dynamic entropy and non-trivial vorticity. In our prior work, we proved that the so…
A quasilinear wave with a supersonic shock in a weak solution interrupting the classical development
Leonardo Abbrescia, Pieter Blue, Jan Sbierski +1
We study the Cauchy problem for classical and weak shock-forming solutions to a model quasilinear wave equation in dimensions arising from a convenient choice of …
The relativistic Euler equations: ESI notes on their geo-analytic structures and implications for shocks in and multi-dimensions
Leonardo Abbrescia, Jared Speck
In this article, we provide notes that complement the lectures on the relativistic Euler equations and shocks that were given by the second author at the program Mathematical Persp…
The emergence of the singular boundary from the crease in compressible Euler flow
Leo Abbrescia, Jared Speck
We study the Cauchy problem for the compressible Euler equations under an arbitrary equation of state with positive speed of sound, aside from that of a Chaplygin gas. For ope…
Remarkable localized integral identities for compressible Euler flow and the double-null framework
Leonardo Abbrescia, Jared Speck
We derive new, localized geometric integral identities for solutions to the compressible Euler equations under an arbitrary equation of state when the sound speed is positive.…
Geometric analysis of 1+1 dimensional quasilinear wave equations
Leonardo Enrique Abbrescia, Willie Wai Yeung Wong
We prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not-necessari…
Global stability of some totally geodesic wave maps
Leonardo Enrique Abbrescia, Yuan Chen
We prove that wave maps that factor as , subject to a sign condition, are globally nonlinear…
Global versions of Gagliardo-Nirenberg-Sobolev inequality and applications to wave and Klein-Gordon equations
Leonardo Abbrescia, Willie Wai Yeung Wong
We prove global, or space-time weighted, versions of the Gagliardo-Nirenberg interpolation inequality, with () endpoint, adapted to a hyperboloidal foliation. The…
Global nearly-plane-symmetric solutions to the membrane equation
Leonardo Abbrescia, Willie Wai Yeung Wong
We prove that any simple planar travelling wave solution to the membrane equation in spatial dimension with bounded spatial extent is globally nonlinearly stable under s…
Reeb Dynamics of the Link of the Singularity
Leonardo Enrique Abbrescia, Irit Huq-Kuruvilla, Jo Nelson +1
The link of the singularity, admits a natural contact structure coming from the set of complex tangencies. The canonical contact form $α_…