4 citations · 11 across the 20 of their papers we have counts for
24 papers
Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model
Jonas Luhrmann, José M. Palacios, Fabio Pusateri +2
We prove asymptotic stability of the degree-one vortex in the -dimensional abelian Yang-Mills-Higgs model at the self-dual coupling, for small equivariant perturbations in w…
Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model: Linear Theory
Jonas Luhrmann, José M. Palacios, Fabio Pusateri +2
We study the linearized dynamics near the degree-one vortex of the -dimensional abelian Yang-Mills-Higgs model at the self-dual coupling, restricted to equivariant perturbat…
Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model: Spectral Theory and Numerics
Jonas Luhrmann, José M. Palacios, Fabio Pusateri +2
This is the first of three papers proving asymptotic stability of the degree-one vortex under equivariant perturbations in the -dimensional abelian Yang-Mills-Higgs model at…
The distorted Fourier transform for the linearized Gross-Pitaevskii equation in the Hyperbolic plane
Oussama Landoulsi, Sohrab Shahshahani
Motivated by the stability problem for Ginzburg-Landau vortices on the hyperbolic plane, we develop the distorted Fourier transform for a general class of radial non-self-adjoint m…
Equivariant stability of vortices in Manton's Chern-Simons-Schrödinger system on the hyperbolic plane
Oussama Landoulsi, Sohrab Shahshahani
In this work we study magnetic vortices on the hyperbolic plane for a Chern-Simons-Schrödinger system introduced by Manton. The model can be thought of as the Schrödinger analogue…
On the Gross-Pitaevskii evolution linearized around the degree-one vortex
Jonas Luhrmann, Wilhelm Schlag, Sohrab Shahshahani
We study the evolution of the Gross-Pitaevskii equation linearized around the Ginzburg-Landau vortex of degree one under equivariant symmetry. Among the main results of this work,…
Stability of the 3-dimensional catenoid for the hyperbolic vanishing mean curvature equation
Sung-Jin Oh, Sohrab Shahshahani
We prove that the -dimensional catenoid is asymptotically stable as a solution to the hyperbolic vanishing mean curvature equation in Minkowski space, modulo suitable translatio…
Stability of the Catenoid for the Hyperbolic Vanishing Mean Curvature Equation Outside Symmetry
Jonas Luhrmann, Sung-Jin Oh, Sohrab Shahshahani
We study the problem of stability of the catenoid, which is an asymptotically flat rotationally symmetric minimal surface in Euclidean space, viewed as a stationary solution to the…
Well-posedness for the free boundary hard phase model in general relativity
Shuang Miao, Sohrab Shahshahani
The hard phase model describes a relativistic barotropic and irrotational fluid with sound speed equal to the speed of light. In the framework of general relativity, the fluid, as…
Well-posedness of the free boundary hard phase fluids in Minkowski background and its Newtonian limit
Shuang Miao, Sohrab Shahshahani, Sijue Wu
The hard phase model describes a relativistic barotropic irrotational fluid with sound speed equal to the speed of light. In this paper, we prove the local well-posedness for this…
Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane Under the Schrödinger Maps Evolution
Andrew Lawrie, Jonas Lührmann, Sung-Jin Oh +1
We consider the Cauchy problem for the Schrödinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studie…
Local smoothing estimates for Schrödinger equations on hyperbolic space
Andrew Lawrie, Jonas Luhrmann, Sung-Jin Oh +1
We establish global-in-time frequency localized local smoothing estimates for Schrödinger equations on hyperbolic space . In the presence of symmetric first and zerot…
On tidal energy in Newtonian two-body motion
Shuang Miao, Sohrab Shahshahani
In this work, which is based on an essential linear analysis carried out by Christodoulou, we study the evolution of tidal energy for the motion of two gravitating incompressible f…
On the Motion of a Self-Gravitating Incompressible Fluid with Free Boundary and Constant Vorticity: An Appendix
Lydia Bieri, Shuang Miao, Sohrab Shahshahani +1
In a recent work [1] the authors studied the dynamics of the interface separating a vacuum from an inviscid incompressible fluid, subject to the self-gravitational force and neglec…
On the Motion of a Self-Gravitating Incompressible Fluid with Free Boundary
Lydia Bieri, Shuang Miao, Sohrab Shahshahani +1
We consider the motion of the interface separating a vacuum from an inviscid, incompressible, and irrotational fluid, subject to the self-gravitational force and neglecting surface…
The Cauchy problem for wave maps on hyperbolic space in dimensions
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
We establish global well-posedness and scattering for wave maps from -dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small i…
Equivariant Wave Maps on the Hyperbolic Plane with Large Energy
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space into surfaces of revolution that was initiated in [13, 14]. When the target is t…
Gap Eigenvalues and Asymptotic Dynamics of Geometric Wave Equations on Hyperbolic Space
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
In this paper we study -equivariant wave maps from the hyperbolic plane into the -sphere as well as the energy critical equivariant Yang-Mills problem on -dimensio…
Profile decompositions for wave equations on hyperbolic space with applications
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
The goal for this paper is twofold. Our first main objective is to develop Bahouri-Gerard type profile decompositions for waves on hyperbolic space. Recently, such profile decompos…
Asymptotic properties of solutions of the Maxwell Klein Gordon equation with small data
Lydia Bieri, Shuang Miao, Sohrab Shahshahani
We prove peeling estimates for the small data solutions of the Maxwell Klein Gordon equations with non-zero charge and with a non-compactly supported scalar field, in dimen…
Stability of stationary equivariant wave maps from the hyperbolic plane
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
In this paper we initiate the study of equivariant wave maps from 2d hyperbolic space into rotationally symmetric surfaces. This problem exhibits markedly different phenomena than…
Blow up for critical wave equations on curved backgrounds
Joules Nahas, Sohrab Shahshahani
We extend the slow blow up solutions of Krieger, Schlag, and Tataru to semilinear wave equations on a curved background. In particular, for a class of manifolds we show the…
Stability of Stationary Wave Maps from a Curved Background to a Sphere
Sohrab M. Shahshahani
We study time and space equivariant wave maps from $M\times\RR\rightarrow S^2,$ where is diffeomorphic to a two dimensional sphere and admits an action of SO(2) by isometries.…
Renormalization and blow up for wave maps from $S^2\times \RR$ to
Sohrab Shahshahani
We construct a one parameter family of finite time blow ups to the co-rotational wave maps problem from $S^2\times \RR$ to parameterized by The longitudinal f…