Related papers: 2D magnetic stability
In continuation of the study of the companion work, we prove the high-energy mode stability for linearized operator around self-similar profiles in [Bahri-Martel-Rapha\"el, 2021] for slightly mass-supercritical NLS in $1 \le d \le 10$. This…
Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…
In a previous paper [JCAP06, 033 (2018)] we have proved that it is possible to have a stable false vacuum in a potential that is unbounded from below. In this paper we discuss the Physics related to our theoretical and numerical results. We…
We present a unified treatment of classical solutions of noncommutative gauge theories. We find all solutions of the noncommutative Yang-Mills equations in 2 dimensions; and show that they are labelled by two integers -- the rank of gauge…
We consider the nonlinear focusing Klein-Gordon equation in $1 + 1$ dimensions and the global space-time dynamics of solutions near the unstable soliton. Our main result is a proof of optimal decay, and local decay, for even perturbations…
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that…
We introduce a two-component system which models a pseudospinor Bose-Einstein condensate (BEC), with a microwave field coupling its two components. The feedback of BEC of the field (the local-field effect) is taken into account by dint of…
In this article we consider the stability threshold of the 2D magnetohydrodynamics (MHD) equations near a combination of Couette flow and large constant magnetic field. We study the partial dissipation regime with full viscous and only…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
We define a Chern- Simons Lagrangian for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. We propose exact N-body eigenstates, set up a…
In the framework of the Ginzburg-Landau approach, we present a self-consistent theory of specific soliton states in mesoscopic (thin-walled) two-band-superconducting cylinders in external parallel magnetic fields. Such states arise in the…
We establish the asymptotic stability of multi-solitons for the one-dimensional Landau-Lifshitz equation with an easy-plane anisotropy. The solitons have non-zero speed, are ordered according to their speeds and have sufficiently separated…
For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian, we prove that the inclusion of the interaction with the self-generated magnetic field leads to instability for all positive values of the fine structure constant.…
We study the quantum stability of Type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is broken {\it \`a la} Scherk-Schwarz (SS) by twisting periodicity conditions…
Given the scarcity of experimentally confirmed magnetic structures, the reliable prediction of magnetic ground states is crucial; however, it remains a long-sought challenge because of the complex magnetic potential energy landscape. Here,…
We study the energetic and dynamic stability of coreless vortices in nonrotated spin-1 Bose-Einstein condensates, trapped with a three-dimensional optical potential and a Ioffe-Pritchard field. The stability of stationary vortex states is…
We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…
(abbreviated) The statistical mechanics of self-gravitating systems is a long-held puzzle. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the…
Self-consistent solutions of the Ginzburg-Landau system of equations, which describe the order parameter and the magnetic field distribution in a long superconducting cylinder of finite radius R, in external magnetic field H, when vortex…
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…