Low regularity well-posedness for Gross-Neveu equations

Hyungjin Huh; Bora  Moon

doi:10.3934/cpaa.2015.14.1903

Article Contents

2015, Volume 14, Issue 5: 1903-1913. Doi: 10.3934/cpaa.2015.14.1903

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Low regularity well-posedness for Gross-Neveu equations

Hyungjin Huh^1, and
Bora Moon^1,

1.
Department of Mathematics, Chung-Ang University, Seoul 156-756

Received: September 30, 2014

Revised: January 31, 2015

Published: August 2015

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Abstract

We address the problem of local and global well-posedness of Gross-Neveu (GN) equations for low regularity initial data. Combined with the standard machinery of $X_R$, $Y_R$ and $X^{s,b}$ spaces, we obtain local-wellposedness of (GN) for initial data $u, v \in H^s$ with $s\geq 0$. To prove the existence of global solution for the critical space $L^2$, we show non concentration of $L^2$ norm.

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Mathematics Subject Classification: Primary: 35L15, 35L45; Secondary: 35Q40, 35F25.

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