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math.AP2022
Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system
Shinya Kinoshita, Shohei Nakamura, Akansha Sanwal
In this paper, we establish local well-posedness for the Zakharov system on , in a low regularity setting. Our result improves the work of Kishimoto. Moreover…
math.AP2022
Sharp well-posedness for the Cauchy problem of the two dimensional quadratic nonlinear Schrödinger equation with angular regularity
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
This paper is concerned with the Cauchy problem of the quadratic nonlinear Schrödinger equation in with the nonlinearity where $η\in \math…