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Related papers: Small Data Wave Maps in Cyclic Spacetime

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We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…

General Relativity and Quantum Cosmology · Physics 2011-06-16 Philippe G. LeFloch , John M. Stewart

We consider the problem of small data global existence for quasilinear wave equations with null condition on a class of Lorentzian manifolds $(\mathbb{R}^{3+1}, g)$ with \textbf{time dependent} inhomogeneous metric. We show that…

Analysis of PDEs · Mathematics 2015-06-18 Shiwu Yang

In this paper, we study the characteristic initial value problem for a class of nonlinear wave equations with data on a conic light cone in the Minkowski space $\mathbb{R}^{1+3}$. We show the existence of local solution for a class of…

Analysis of PDEs · Mathematics 2025-04-03 Wei Dai , Shiwu Yang

We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a…

Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space-time with multiple timelike…

Quantum Physics · Physics 2017-11-22 Matthias Lienert , Sören Petrat , Roderich Tumulka

The two-sphere valued wave map flow on a Lorentzian domain R x Sigma, where Sigma is any flat two-torus, is studied. The Cauchy problem with initial data tangent to the moduli space of holomorphic maps Sigma -> S^2 is considered, in the…

Differential Geometry · Mathematics 2015-09-14 J. M. Speight

We examine the interaction between floating cylindrical objects and surface waves in the gravity regime. Since the impact of resonance phenomena associated with floating bodies, particularly at laboratory scales, remains underexplored, we…

We consider the wave equation, $\square_g\psi=0$, in fixed flat Friedmann-Lema\^itre-Robertson-Walker and Kasner spacetimes with topology $\mathbb{R}_+\times\mathbb{T}^3$. We obtain generic blow up results for solutions to the wave equation…

General Relativity and Quantum Cosmology · Physics 2018-06-04 Artur Alho , Grigorios Fournodavlos , Anne T. Franzen

We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants we consider the characteristic form of these equations. In a first part, we show that the resulting constraint…

Analysis of PDEs · Mathematics 2016-03-08 André Lisibach

We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we…

Analysis of PDEs · Mathematics 2024-04-03 Kiril Datchev , Jacob Shapiro

This paper presents a solution to an initial value problem for the 1-dimensional wave equation on time scales through the application of a Fourier transform and its inverse via contour integrals. The time scale of the spatial dimension is…

Analysis of PDEs · Mathematics 2024-09-26 Davis Funk , Charis Tsikkou

Sufficient conditions for the well-posedness of the initial value problem for the scalar wave equation are obtained in space-times with hypersurface singularities

General Relativity and Quantum Cosmology · Physics 2009-09-25 J. A. Vickers , J. P. Wilson

We cast the four-dimensional field equations of the Nonsymmetric Gravitational Theory (NGT) into a form appropriate for numerical study. In doing so, we have restricted ourselves to spherically symmetric spacetimes, and we have kept only…

General Relativity and Quantum Cosmology · Physics 2007-05-23 M. A. Clayton , L. Demopoulos , J. Legare

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…

Optics · Physics 2009-10-31 R. de la Llave , N. Petrov

We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width $\epsilon$. Motivated by applications to surface wave propagation phenomena, we study…

Spectral Theory · Mathematics 2013-12-19 Fedor Bakharev , Keijo Ruotsalainen , Jari Taskinen

For 2 + 1 dimensional wave maps with $\mathbb{S}^2$ as the target, we show that for all positive numbers $T_0 > 0$ and $E_0 > 0$, there exist Cauchy initial data with energy at least $E_0$, so that the solution's life-span is at least…

Analysis of PDEs · Mathematics 2012-07-25 Jinhua Wang , Pin Yu

We consider the energy critical Schrodinger map to the 2-sphere for equivariant initial data of homotopy number k=1. We show the existence of a set of smooth initial data arbitrarily close to the ground state harmonic map in the scale…

Analysis of PDEs · Mathematics 2011-02-25 Frank Merle , Pierre Raphael , Igor Rodnianski

The formulation of the Einstein field equations admitting two Killing vectors in terms of harmonic mappings of Riemannian manifolds is a subject in which Charlie Misner has played a pioneering role. We shall consider the hyperbolic case of…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Y. Nutku

We study deformations of axially symmetric initial data for Einstein-Maxwell equations satisfying the time-rotation ($t$-$\phi$) symmetry and containing one asymptotically cylindrical end and one asymptotically flat end. We find that the…

General Relativity and Quantum Cosmology · Physics 2016-05-25 Andrés Aceña , María E. Gabach Clément

The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown…

Mathematical Physics · Physics 2018-05-01 Umberto Lupo