Kazumasa Fujiwara

Finite time blowup of solutions to the nonlinear Schrödinger equation without gauge invariance

A lifespan estimate and a condition of the initial data for finite time blowup for the nonlinear Schrodinger equation are presented from a view point of ordinary differential equation (ODE) mechanism.

Stability of the Young and Hölder inequalities

We give a simple proof of the Aldaz stability version of the Young and Hölder inequalities and further refinements of available stability versions of those inequalities.MSC:26D15.

Higher Order Fractional Leibniz Rule

The fractional Leibniz rule is generalized by the Coifman–Meyer estimate. It is shown that the arbitrary redistribution of fractional derivatives for higher order with the corresponding correction terms.

On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation

An explicit lifespan estimate is presented for the derivative Schrodinger equations with periodic boundary condition.