Stability of spherically symmetric wave maps / Joachim Krieger.

Format:

Book

Author/Creator:

Krieger, Joachim, 1976- author.

Series:

Memoirs of the American Mathematical Society ; no. 853.

Memoirs of the American Mathematical Society, 0065-9266 ; number 853

Language:

English

Subjects (All):

Wave equation.

Differential equations, Parabolic.

Physical Description:

1 online resource (96 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2006]

Language Note:

English

Summary:

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 respect to some $H^{1+\mu}$, $\mu>0$. We show that such Wave Maps don't develop singularities in finite time and stay close to the Wave Map extending the spherically symmetric data(whose existence is ensured by a theorem of Christodoulou-Tahvildar-Zadeh) with respect to all $H^{1+\delta}, \delta\less\mu_{0}$ for suitable $\mu_{0}(\mu)>0$. We obtain a similar result for Wave Maps whose initial data are close to geodesic ones. This strengthens a theorem of Sideris for this context.

Contents:

""Contents""; ""Preface""; ""Chapter 1. Introduction, Controlling Spherically Symmetric Wave Maps""; ""1.1. Introduction""; ""1.2. A priori estimates for spherically symmetric Wave Maps""; ""1.3. The perturbation argument""; ""Chapter 2. Technical Preliminaries. Proofs of Main Theorems""; ""Chapter 3. The Proof of Proposition 2.2""; ""Chapter 4. Proof of Theorem 2.3""; ""Bibliography""

Notes:

"Volume 181, number 853 (second of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0457-5