Near soliton evolution for equivariant Schrodinger maps in two spatial dimensions / Ioan Bejenaru, Daniel Tataru.

Format:

Book

Author/Creator:

Bejenaru, Ioan, 1974- author.

Tataru, Daniel, 1967- author.

Series:

Memoirs of the American Mathematical Society ; Volume 228, Number 1069.

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 228, Number 1069

Language:

English

Subjects (All):

Heat equation.

Schr©œdinger equation.

Differential equations, Parabolic.

Physical Description:

1 online resource (120 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2013.

Language Note:

English

Summary:

The authors consider the Schrodinger Map equation in 2+1 dimensions, with values into Si 1/2. 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 ?'. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology XC?'."

Contents:

""7.3. The transition from ( , , ) to â??, â?? and """"7.4. The transition from to ( â??, â??).""; ""7.5. The transition from , â?? and â?? to ( , , )""; ""7.6. Local energy bounds""; ""Chapter 8. The nonlinear equation for ""; ""8.1. A short time result""; ""8.2. The long time result""; ""Chapter 9. The bootstrap estimate for the Å? parameter.""; ""Chapter 10. The bootstrap argument""; ""10.1. Regular solutions""; ""10.2. Rough solutions""; ""Chapter 11. The ¹ instability result""; ""Bibliography""

Notes:

"Volume 228, Number 1069 (first of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1481-3