Differential and Integral Equations

Local and global well posedness for the Chern-Simons-Dirac system in one dimension

Nikolaos Bournaveas, Timothy Candy, and Shuji Machihara

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Abstract

We consider the Cauchy problem for the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+1}$ with initial data in $H^s$. Almost optimal local well posedness is obtained. Moreover, we show that the solution is global in time, provided that initial data for the spinor component has finite charge, or $L^2$ norm.

Article information

Source
Differential Integral Equations, Volume 25, Number 7/8 (2012), 699-718.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012659

Mathematical Reviews number (MathSciNet)
MR2975691

Zentralblatt MATH identifier
1265.35278

Subjects
Primary: 35Q41: Time-dependent Schrödinger equations, Dirac equations 35A01: Existence problems: global existence, local existence, non-existence

Citation

Bournaveas, Nikolaos; Candy, Timothy; Machihara, Shuji. Local and global well posedness for the Chern-Simons-Dirac system in one dimension. Differential Integral Equations 25 (2012), no. 7/8, 699--718. https://projecteuclid.org/euclid.die/1356012659


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