32 citations · 178 across the 24 of their papers we have counts for
6 papers · 1 filter
A remark on norm inflation for nonlinear wave equations
Justin Forlano, Mamoru Okamoto
In this note, we study the ill-posedness of nonlinear wave equations (NLW). Namely, we show that NLW experiences norm inflation at every initial data in negative Sobolev spaces. Th…
Two floating camphor particles interacting through lateral capillary force
Yuhei Hirose, Yusuke Yasugahira, Mamoru Okamoto +4
We consider a mathematical model for a two-particle system driven by the spatial gradient of a concentration field of chemicals with conservative attractive interactions in one dim…
Comparing the stochastic nonlinear wave and heat equations: a case study
Tadahiro Oh, Mamoru Okamoto
We study the two-dimensional stochastic nonlinear wave equation (SNLW) and stochastic nonlinear heat equation (SNLH) with a quadratic nonlinearity, forced by a fractional derivativ…
A remark on triviality for the two-dimensional stochastic nonlinear wave equation
Tadahiro Oh, Mamoru Okamoto, Tristan Robert
We consider the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In particular, we investigate the…
On the stochastic nonlinear Schrödinger equations at critical regularities
Tadahiro Oh, Mamoru Okamoto
We consider the Cauchy problem for the defocusing stochastic nonlinear Schrödinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By ada…
Scattering for the one-dimensional Klein-Gordon equation with exponential nonlinearity
Masahiro Ikeda, Takahisa Inui, Mamoru Okamoto
We consider the asymptotic behavior of solutions to the Cauchy problem for the defocusing nonlinear Klein-Gordon equation (NLKG) with exponential nonlinearity in the one spatial di…