17 citations · 83 across the 17 of their papers we have counts for
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Well-posedness for KdV-type equations with quadratic nonlinearity
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
We consider the Cauchy problem of the KdV-type equation \[ \partial_t u + \frac{1}{3} \partial_x^3 u = c_1 u \partial_x^2u + c_2 (\partial_x u)^2, \quad u(0)=u_0. \] Pilod (2008) s…
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with radial initial data
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations. This system was introduced by M. Colin and T. Colin (200…
Sharp bilinear estimates and its application to a system of quadratic derivative nonlinear Schrödinger equations
Hiroyuki Hirayama, Shinya Kinoshita
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations for the spatial dimension and . This system was…