2 citations · 3 across the 6 of their papers we have counts for
7 papers
A sharp criterion for well-posedness of semilinear Schrödinger equations on the real line
Toshiki Kondo, Mamoru Okamoto
We consider the Cauchy problem for semilinear Schrödinger equations on the real line. We establish a sharp necessary and sufficient condition on the nonlinearity for local well-pos…
Norm inflation for quadratic derivative fractional nonlinear Schrödinger equations
Toshiki Kondo, Mamoru Okamoto
We consider the Cauchy problem for quadratic derivative fractional nonlinear Schrödinger equations on or . We determine the sharp exponents of the fraction…
Well- and Ill-posedness of the Cauchy problem for derivative fractional nonlinear Schrödinger equations on the torus
Takamori Kato, Toshiki Kondo, Mamoru Okamoto
We consider the Cauchy problem for derivative fractional Schrödinger equations (fNLS) on the torus . Recently, the second and third authors established a necessary and s…
Well- and ill-posedness of the Cauchy problem for semi-linear Schrödinger equations on the torus
Toshiki Kondo, Mamoru Okamoto
We consider the Cauchy problem for semi-linear Schrödinger equations on the torus . We establish a necessary and sufficient condition on the polynomial nonlinearity for…
Norm inflation for a higher-order nonlinear Schrödinger equation with a derivative on the circle
Toshiki Kondo, Mamoru Okamoto
We consider a periodic higher-order nonlinear Schrödinger equation with the nonlinearity , where is a natural number. We prove the norm inflation in a subspac…
Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus
Guopeng Li, Mamoru Okamoto, Liying Tao
We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schrödinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt…
Well-posedness and ill-posedness for a system of periodic quadratic derivative nonlinear Schrödinger equations
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
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 i…