Global Regularity For The Yang Mills Equations On High Dimensional Minkowski Space

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Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space

Joachim Krieger,Jacob Sterbenz
Global Regularity for the Yang Mills Equations on High Dimensional Minkowski Space Book PDF

Author : Joachim Krieger,Jacob Sterbenz
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 49,8 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780821844892

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Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space by Joachim Krieger,Jacob Sterbenz Pdf

This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on $(6+1)$ and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space $\dot{H}_A^{(n-4)/{2}}$. Regularity is obtained through a certain ``microlocal geometric renormalization'' of the equations which is implemented via a family of approximate null Cronstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic $L^p$ spaces, and also proving some bilinear estimates in specially constructed square-function spaces.

Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces

David Dos Santos Ferreira,Wolfgang Staubach
Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces Book PDF

Author : David Dos Santos Ferreira,Wolfgang Staubach
Publisher : American Mathematical Soc.
Page : 65 pages
File Size : 46,7 Mb
Release : 2014-04-07
Category : Mathematics
ISBN : 9780821891193

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Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces by David Dos Santos Ferreira,Wolfgang Staubach Pdf

The authors investigate the global continuity on spaces with of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in with . They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted spaces, with and (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition.

On the Regularity of the Composition of Diffeomorphisms

H. Inci,Thomas Kappeler,P. Topalov
On the Regularity of the Composition of Diffeomorphisms Book PDF

Author : H. Inci,Thomas Kappeler,P. Topalov
Publisher : American Mathematical Soc.
Page : 60 pages
File Size : 49,5 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887417

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On the Regularity of the Composition of Diffeomorphisms by H. Inci,Thomas Kappeler,P. Topalov Pdf

For $M$ a closed manifold or the Euclidean space $\mathbb{R}^n$, the authors present a detailed proof of regularity properties of the composition of $H^s$-regular diffeomorphisms of $M$ for $s >\frac{1}{2}\dim M+1$.

Near Soliton Evolution for Equivariant Schrödinger Maps in Two Spatial Dimensions Ioan Bejenaru, University of California, San Diego, La Jolla, CA, and Daniel Tataru, University of California, Berkeley, Berkeley, CA

Ioan Bejenaru,Daniel Tataru
Near Soliton Evolution for Equivariant Schr dinger Maps in Two Spatial Dimensions Ioan Bejenaru University of California San Diego La Jolla CA and Daniel Tataru University of California Berkeley Berkeley CA Book PDF

Author : Ioan Bejenaru,Daniel Tataru
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 42,7 Mb
Release : 2014-03-05
Category : Mathematics
ISBN : 9780821892152

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Near Soliton Evolution for Equivariant Schrödinger Maps in Two Spatial Dimensions Ioan Bejenaru, University of California, San Diego, La Jolla, CA, and Daniel Tataru, University of California, Berkeley, Berkeley, CA by Ioan Bejenaru,Daniel Tataru Pdf

The authors consider the Schrödinger Map equation in 2+1 dimensions, with values into \mathbb{S}^2. This admits a lowest energy steady state Q, namely the stereographic projection, which extends to a two dimensional family of steady states by scaling and rotation. The authors prove that Q is unstable in the energy space \dot H^1. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology X \subset \dot H^1.

Operator Theory, Operator Algebras, and Applications

Alejandro D. de Acosta,Peter Ney
Operator Theory Operator Algebras and Applications Book PDF

Author : Alejandro D. de Acosta,Peter Ney
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 45,6 Mb
Release : 2014-03-05
Category : Mathematics
ISBN : 9780821890899

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Operator Theory, Operator Algebras, and Applications by Alejandro D. de Acosta,Peter Ney Pdf

Strange Attractors for Periodically Forced Parabolic Equations

Kening Lu,Qiudong Wang,Lai-Sang Young
Strange Attractors for Periodically Forced Parabolic Equations Book PDF

Author : Kening Lu,Qiudong Wang,Lai-Sang Young
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 49,9 Mb
Release : 2013-06-28
Category : Mathematics
ISBN : 9780821884843

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Strange Attractors for Periodically Forced Parabolic Equations by Kening Lu,Qiudong Wang,Lai-Sang Young Pdf

The authors prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.

The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates

Robert J. Buckingham,Peter D. Miller
The Sine Gordon Equation in the Semiclassical Limit Dynamics of Fluxon Condensates Book PDF

Author : Robert J. Buckingham,Peter D. Miller
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 51,6 Mb
Release : 2013-08-23
Category : Mathematics
ISBN : 9780821885451

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The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates by Robert J. Buckingham,Peter D. Miller Pdf

The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.

Weighted Bergman Spaces Induced by Rapidly Increasing Weights

Jose Angel Pelaez,Jouni Rattya
Weighted Bergman Spaces Induced by Rapidly Increasing Weights Book PDF

Author : Jose Angel Pelaez,Jouni Rattya
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 50,7 Mb
Release : 2014-01-08
Category : Mathematics
ISBN : 9780821888025

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Weighted Bergman Spaces Induced by Rapidly Increasing Weights by Jose Angel Pelaez,Jouni Rattya Pdf

Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms

Andrew Knightly,C. Li
Kuznetsov s Trace Formula and the Hecke Eigenvalues of Maass Forms Book PDF

Author : Andrew Knightly,C. Li
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 46,6 Mb
Release : 2013-06-28
Category : Mathematics
ISBN : 9780821887448

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Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms by Andrew Knightly,C. Li Pdf

The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.

On Some Aspects of Oscillation Theory and Geometry

Bruno Bianchini,Luciano Mari,Marco Rigoli
On Some Aspects of Oscillation Theory and Geometry Book PDF

Author : Bruno Bianchini,Luciano Mari,Marco Rigoli
Publisher : American Mathematical Soc.
Page : 195 pages
File Size : 43,6 Mb
Release : 2013-08-23
Category : Mathematics
ISBN : 9780821887998

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On Some Aspects of Oscillation Theory and Geometry by Bruno Bianchini,Luciano Mari,Marco Rigoli Pdf

The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

On the Steady Motion of a Coupled System Solid-liquid

Josef Bemelmans,Giovanni Paolo Galdi,Mads Kyed
On the Steady Motion of a Coupled System Solid liquid Book PDF

Author : Josef Bemelmans,Giovanni Paolo Galdi,Mads Kyed
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 41,6 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887738

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On the Steady Motion of a Coupled System Solid-liquid by Josef Bemelmans,Giovanni Paolo Galdi,Mads Kyed Pdf

The authors study the unconstrained (free) motion of an elastic solid $\mathcal B$ in a Navier-Stokes liquid $\mathcal L$ occupying the whole space outside $\mathcal B$, under the assumption that a constant body force $\mathfrak b$ is acting on $\mathcal B$. More specifically, the authors are interested in the steady motion of the coupled system $\{\mathcal B,\mathcal L\}$, which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. The authors prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of $\mathcal B$ satisfies suitable geometric properties.

Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds

Jose Luis Flores,J. Herrera,M. Sánchez
Gromov Cauchy and Causal Boundaries for Riemannian Finslerian and Lorentzian Manifolds Book PDF

Author : Jose Luis Flores,J. Herrera,M. Sánchez
Publisher : American Mathematical Soc.
Page : 76 pages
File Size : 55,5 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887752

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Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds by Jose Luis Flores,J. Herrera,M. Sánchez Pdf

Recently, the old notion of causal boundary for a spacetime $V$ has been redefined consistently. The computation of this boundary $\partial V$ on any standard conformally stationary spacetime $V=\mathbb{R}\times M$, suggests a natural compactification $M_B$ associated to any Riemannian metric on $M$ or, more generally, to any Finslerian one. The corresponding boundary $\partial_BM$ is constructed in terms of Busemann-type functions. Roughly, $\partial_BM$ represents the set of all the directions in $M$ including both, asymptotic and ``finite'' (or ``incomplete'') directions. This Busemann boundary $\partial_BM$ is related to two classical boundaries: the Cauchy boundary $\partial_{C}M$ and the Gromov boundary $\partial_GM$. The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification $M_B$, relating it with the previous two completions, and (3) to give a full description of the causal boundary $\partial V$ of any standard conformally stationary spacetime.