Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with low regularity periodic initial data

2013/11/24 by Hiroyuki Hirayama, Hirayama, Hiroyuki
Mathematics · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1311.6102

Abstract

We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. For the nonperiodic case, the author proved the small data global well-posedness and the scattering at the scaling critical regularity for d≥ 2 when the coefficients of Laplacian satisfy some condition. In the present paper, we prove the well-posedness of the system for the periodic case. In particular, well-posedness is proved at the scaling critical regularity for d≥ 3 under some condition for the coefficients of Laplacian.

Related

• Well-posedness and ill-posedness for a system of periodic quadratic derivative nonlinear Schrödinger equations
• Local well-posedness for a system of quadratic derivative nonlinear Schrödinger equations
• Quadratic Nonlinear Derivative Schrödinger Equations - Part 2
• Quadratic Nonlinear Derivative Schrödiger Equations - Part 1
• On the low-regularity global well-posedness of a system of nonlinear Schrodinger Equation