Lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order

Abstract

This paper is concerned with the upper bound of the lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order. In [8], Masaki and the first author obtain the upper bound of the lifespan of solutions to our equation via a test function method introduced by [16, 17]. Their nonlinearity contains a non-oscillating term $|u{|}^{1+2/d}$ which causes difficultly for constructing an even small data global solution. The non-oscillating term corresponds to the $L^1$-scaling critical. In this paper, it turns out that the upper bound can be refined by employing an unified test function by Ikeda and the second author [5].

9 pages

References in corpus (1)

• Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions

Cited by in corpus (1)

• Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance