Analyticity of solutions to a quadratic system of Schrodinger equations without mass resonance condition

作者：Hoshino Gaku^*

来源：Journal of Mathematical Analysis and Applications, 2018, 467(1): 331-348.

DOI：10.1016/j.jmaa.2018.07.009

• Nonlinear Schrodinger equations
• Analyticity
• Global existence
• Analytic Hardy space
• Test functions of Fourier hyperfunctions

We consider the Cauchy problem for a quadratic system of Schrodinger equations in space dimensions n >= 4 without mass resonance condition. Analytic smoothing effect for the quadratic system of Schrodinger equations under the mass resonance condition for data which satisfy exponentially decaying condition has been studied in [14]. In this study, we construct global solutions in the analytic Hardy space via the phase modulation operator, based on the scale critical Sobolev space ((H) over dot)(n/2-2) with data like the test functions of Fourier hyperfunctions, under the condition m(1) <= m(2) <= (1 + 4/n) m(1) between two masses m(1) and m(2).

• 出版日期2018-11-1