Satoshi Masaki

Large data mass-subcritical NLS: critical weighted bounds imply scattering

We consider the mass-subcritical nonlinear Schrödinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity

Refinement of Strichartz Estimates for Airy Equation in Nondiagonal Case and its Application

s_c\in (\max \{-1,-\frac{d}{2}\},0)

Two minimization problems on non-scattering solutions to mass-subcritical nonlinear Schr\"odinger equation

sc∈(max{-1,-d2},0), we prove that any solution satisfying

Remarks on global existence of classical solution to multi-dimensional compressible Euler-Poisson equations with geometrical symmetry

\begin{aligned} \left\| \, |x|^{|s_c|}e^{-it\Delta } u\right\| _{L_t^\infty L_x^2} <\infty \end{aligned}

Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions

|x||sc|e-itΔuLt∞Lx2<∞on its maximal interval of existence must be global and scatter.

Refinement of Strichartz estimate for Airy equation in non-diagonal case and its application

In this paper, we consider the final state problem for the nonlinear Schrodinger equation with a homogeneous nonlinearity of the critical order which is not necessarily a polynomial. In [10], the first and the second authors consider one- and two-dimensional cases and gave a sufficient condition on the nonlinearity for that the corresponding equation admits a solution that behaves like a free solution with or without a logarithmic phase correction. The present paper is devoted to the study of the three-dimensional case, in which it is required that a solution converges to a given asymptotic profile in a faster rate than in the lower dimensional cases. To obtain the necessary convergence rate, we employ the end-point Strichartz estimate and modify a time-dependent regularizing operator, introduced in [10]. Moreover, we present a candidate of the second asymptotic profile to the solution.