Last edited by Bralmaran
Monday, November 23, 2020 | History

4 edition of Stability of Spherically Symmetric Wave Maps (Memoirs of the American Mathematical Society) found in the catalog.

# Stability of Spherically Symmetric Wave Maps (Memoirs of the American Mathematical Society)

Written in English

Subjects:
• Waves & Wave Mechanics,
• Science,
• Mathematics,
• Science/Mathematics,
• Differential equations, Parabolic,
• Wave equation

• The Physical Object
FormatPaperback
Number of Pages80
ID Numbers
Open LibraryOL9814623M
ISBN 100821838776
ISBN 109780821838778

Abstract. We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equation: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term can be taken to lie. Whether the wave function is symmetric or antisymmetric under such operations gives you insight into whether two particles can occupy the same quantum state. Given that P ij 2 = 1, note that if a wave function is an eigenfunction of P ij, then the possible eigenvalues are 1 and –1.

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### Stability of Spherically Symmetric Wave Maps (Memoirs of the American Mathematical Society) by Joachim Krieger Download PDF EPUB FB2

Chapter 1. Introduction, Controlling Spherically Symmetric Wave Maps 1 10 free; Introduction 1 10; A priori estimates for spherically symmetric Wave Maps 4 13 free; The perturbation argument 13 22; Chapter 2.

Technical Preliminaries. Proofs of Main Theorems 15 24; Chapter 3. The Proof of Proposition 31 40; Chapter 4. Proof of. Get this from a library. Stability of spherically symmetric wave maps. [Joachim Krieger] -- We study Wave Maps from ${\mathbf{R}} {2+1}$ to the hyperbolic plane ${\mathbf{H}} {2}$ with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with.

We study Wave Maps from R^{2+1} to the hyperbolic plane with smooth compactly supported initial data which are close to smooth spherically symmetric ones with respect to some H^{1+\mu}, \mu>: Joachim Krieger. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract.

We study Wave Maps from R 2+1 to the hyperbolic plane H 2 with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some H 1+µ, µ> 0. We show that such Wave Maps don’t develop singularities in finite time and stay close to the Wave Map.

Stability of Spherically Symmetric Wave Maps. By Joachim Krieger. We show that such Wave Maps don't develop singularities and stay close to the Wave Map extending the spherically symmetric data with respect to all H^{1+\delta}, \deltaWave Maps whose initial data are close to geodesic : Joachim Krieger.

We study Wave Maps from R^{2+1} to the hyperbolic plane with smooth compactly supported initial data which are close to smooth spherically symmetric ones with respect to some H^{1+\mu}, \mu>0.

We show that such Wave Maps don't develop singularities and stay close to the Wave Map extending the spherically symmetric data with respect to all H^{1+\delta}, \delta<\mu_{0}(\mu). Stability of Spherically Symmetric Wave Maps. By J. Krieger.

Abstract. Abstract. We study Wave Maps from R 2+1 to the hyperbolic plane H 2 with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some H 1+µ, µ> 0.

We show that such Wave Maps don’t develop singularities in. Wave maps are critical points U: M → N of the Lagrangian ℒ︁[U] = ∞ M ‖dU‖ 2, where M is an Einsteinian manifold and N a Riemannian one.

For the case M = ℝ 2,1 and U a spherically symmetric map, it is shown that the solution to Stability of Spherically Symmetric Wave Maps book Cauchy problem for U with smooth initial data of arbitrary size is smooth for all time, provided the target manifold N satisfies the two conditions.

We use our "generalized variational principle", described in a previous work, to analyze the stability of static spherically symmetric solutions to spherically symmetric perturbations in three such alternative theories: Carroll et al.'s f(R) gravity, Jacobson & Mattingly's "Einstein.

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics.

The books of the series are addressed to both experts and advanced students.5/5(1). Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere Piotr Bizon´ Institute of Physics, Jagellonian University, Krak´ow, Poland Aug Abstract We prove existence of a countable family of spherically symmetric self-similar wave maps from 3+1 Minkowski spacetime into the 3-sphere.

These maps can be viewed. After every major earthquake, the Earth rings like a bell for several days. These free oscillations of the Earth and the related propagating body and surface waves are routinely detected at broad-band seismographic stations around the world.

In this book, F. Dahlen and Jeroen Tromp present an advanced theoretical treatment of global seismology, describing the normal-mode, body-wave, and. A stability analysis of a spherically symmetric star in scalar-tensor theories of gravity is given in terms of the frequencies of quasi-normal modes.

We use cookies to enhance your experience on our continuing to use our website, you are agreeing to our use of cookies. On the stability of blowup solutions for the critical corotational wave-map problem.

Joachim Krieger and Shuang Miao Full-text: Access denied (no subscription detected) On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math. 46 (), no. 7, – Shibahashi, H. This book deals primarily with the linear theory of nonradial oscillations of spherically symmetric stars.

A simplified form of the stability equation appropriate for liquids of small viscosity undergoing nearly spherically symmetric flow is derived on the basis of earlier results. This equation is then applied to the analysis of the stability characteristics of the spherical shape for growing and collapsing cavitation bubbles.

It is found that viscosity does not remove the well‐known instability. There is no $$\varphi$$- dependence since with the potential being spherically-symmetric the whole problem is azimuthally-symmetric about the direction of the incoming wave.

It is perhaps worth mentioning that for scattering in just one partial wave, the outgoing current is equal to the ingoing current, whether there is a phase shift or not.

(Asymptotics for spherically symmetric solutions) Let ψ be a spherically symmetric solution to the wave equation on the class of spacetimes (M, g), where g is given by. Let n ∈ N and assume the following additional asymptotics for the metric component D: D (r) = 1 − 2 M r − 1 + ∑ m = 1 n − 1 d m r − m − 1 + O 3 + n (r − n.

TITLE = {Radially symmetric wave maps from {$(1+2)$}-dimensional {M}inkowski space to general targets}, JOURNAL = {Calc. Var. Partial Differential Equations}, FJOURNAL = {Calculus of Variations and Partial Differential Equations}.

We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. for both standing and travelling wave configurations generated by the perturbation.

We investigate the stability of. (with Yan Guo) Formation of singularities in relativistic fluid dynamics and in spherically symmetric plasma dynamics, Contemporary Mathematics, Vol.(). On the stability of stationary wave maps, Comm.

Math. Phys., Vol., (). Stability of periodic waves to gKdV 5 Its second derivative M00 w(u) = J 1T: X 7!ker(J)?is a bounded symmetric linear operator by(3). Note that Mw(T(g)u) = Mw(u), i.e., that Mw is a conserved functional under the group action.

We are now positioned to deﬁne what we mean by relative equilibria of(1). We prove existence of a countable family of spherically symmetric self-similar wave maps from 3+1 Minkowski spacetime into the 3-sphere.

These maps can be viewed as excitations of the ground state. Books. Publishing Support. Login. we investigate the linear stability of black holes and solitons with Yang-Mills hair and a negative cosmological constant.

We show that those solutions which have no linear instabilities under odd- and even-parity spherically symmetric perturbations remain stable under odd-parity, linear, non-spherically.

Parry Spherically Symmetric Static States of Wave Dark Matter This is consistent with the fact that the metric functions, e2V and 1 2M r, are also smooth spherically symmetric functions that are nonzero at r= 0 and hence even functions of r. This implies that, since ris an odd function, M(t;r) must also act like an odd function near r= 0.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We prove existence of a countable family of spherically symmetric self-similar wave maps from 3 + 1 Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state wave map found previously by Shatah.

The first excitation is particularly interesting in the context of the Cauchy. () Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation.

Inverse Problems In the absence of Pauli, multiple electron atoms would be spherically symmetric but the electron distribution within would still show some structure, as does Helium. (Although it is arguable that the structure is simply an artifact of the electron-basis-state representation, and that in the density matrix representation the charge distribution.

Demetrios Christodoulou (Greek: Δημήτριος Χριστοδούλου; born Octo ) is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the Minkowski spacetime of special relativity in the framework of general odoulou is a MacArthur Fellow.

In a spherically symmetric spacetime admitting stably trapped null geodesics in the sense of section, there exists some universal constant such that where by we mean the energy of the wave restricted to the region, the surface is given by, and the supremum is taken over all functions in the completion of the set of smooth, compactly.

An important problem in quantum mechanics is that of a particle in a spherically symmetric potential, i.e., a potential that depends only on the distance between the particle and a defined center particular, if the particle in question is an electron and the potential is derived from Coulomb's law, then the problem can be used to describe a hydrogen-like (one-electron) atom (or ion).

Finally, we discuss how these coordinates and the metric can be used to solve the spherically symmetric Einstein-Klein-Gordon equations. In Chapter 3, we explore spherically symmetric solutions to the Einstein-Klein-Gordon equa-tions, the de ning equations of wave dark matter, where the scalar eld is of the form fpt;rq.

Abstract. Spherically symmetric transonic accretion of a fractal medium has been studied in both the stationary and the dynamic regimes. The stationary transonic solution is greatly sensitive to infinitesimal deviations in the outer boundary condition, but the flow becomes transonic and stable when its evolution is followed through time.

Bundle: Physics for Scientists and Engineers with Modern Physics, 10th + WebAssign Printed Access Card for Serway/Jewett's Physics for Scientists and Engineers, 10th, Single-Term (10th Edition) Edit edition.

Problem 72AP from Chapter This generalizes the results obtained in [47] for the spatially continuous setting. Finally, we prove that the horizontal planar wave is nonlinearly stable with respect to perturbations that are asymptotically periodic in the vertical direction.

Existence and stability of nonisentropic compressible vortex sheets Alessandro Morando, Paola Trebeschi and Tao Wang Spherically symmetric shadow wave solutions to the compressible Euler sys- tem at the origin Marko Nedeljkov, Lukas Neumann and.

1) A particle is in a spherically symmetric potential V(r) 8(r-b). mb in a state where l = 0. a) For E b. Remember the condition that the wave function must not explode at r = 0. (Let k = -2mE/H.) b) Use matching conditions for u(r) at r =b to show that coth Kb. Gordon equation). Speci cally, in this dissertation, we study spherically symmetric wave dark matter and compare these results with observations of dwarf spheroidal galaxies as a rst attempt to compare the implications of the theory of wave dark matter with actual observations of.

On spherically symmetric solutions of the Einstein–Euler equations Makino, Tetu, Kyoto Journal of Mathematics, ; THE CRITICAL MASS OF COMPRESSIBLE VISCOUS GAS-STARS Kuan, Wen-Chi, Taiwanese Journal of Mathematics, ; Time-periodic approximations of the Euler–Poisson system near Lane–Emden stars Jang, Juhi, Analysis & PDE, ; Instability theory of the.

We compute families of spherically symmetric neutron-star models in two-derivative scalar-tensor theories of gravity with a massive scalar field.

The numerical approach we present allows us to compute the resulting spacetimes out to infinite radius using a relaxation algorithm on a compactified grid. It has recently turned out that in molecules and solids a set of spherically symmetric densities determines uniquely the external potential.

Here it is shown that any of the spherically symmetric densities obeys a Schrödinger-like differential equation that is equivalent to the Euler equation of this density.

The exact effective potential is presented explicitly in terms of wave function. In this paper, we present Plane symmetric, Cylindrically Symmetric and Spherically Symmetric Black hole or Vacuum solutions of Einstein Field Equations(EFEs). Some of these solutions are new which we have not seen i n the literature.

This calculation will help us in understanding the gravitational wave and gravitational wave spacetimes.‪Rutgers (New Brunswick)‬ - ‪Cited by 1,‬ - ‪General Relativity‬ - ‪Mathematical Physics‬.