5 papers
Ground states of the defocusing nonlinear Schrödinger equation with a point interaction in dimensions 2 and 3
Masahiro Ikeda, Gustavo de Paula Ramos
This paper is concerned with ground states of the defocusing nonlinear Schrödinger equation with a point interaction, \[ \mathrm{i} \partial_t ψ= -Δ_αψ+ ψ|ψ|^{p - 2} \quad \text{in…
Existence of solutions to the semilinear damped wave equation with non- slowly decaying data : polynomial nonlinearity case
Masahiro Ikeda, Takahisa Inui, Yuta Wakasugi
We study the Cauchy problem of the semilinear damped wave equation with polynomial nonlinearity, and establish the local and global existence of the solution for slowly decaying in…
Dynamics of dissipative solutions to the Hardy-Sobolev parabolic equation
Masahiro Ikeda, César J. Niche, Gabriela Planas
We study the long-time behaviour of solutions to the Hardy-Sobolev parabolic equation in critical function spaces for any spatial dimension . By employing the Fourier spl…
Global dynamics for the energy-critical nonlinear heat equation
Masahiro Ikeda, César J. Niche, Gabriela Planas
We examine the energy-critical nonlinear heat equation in critical spaces for any dimension greater or equal than three. The aim of this paper is two-fold. First, we establish a ne…
Algebraic decay rates for 3D Navier-Stokes and Navier-Stokes-Coriolis equations in
Masahiro Ikeda, Leonardo Kosloff, César J. Niche +1
An algebraic upper bound for the decay rate of solutions to the Navier-Stokes and Navier-Stokes-Coriolis equations in the critical space is…