arXiv:1911.01183 Abstract | arXiv Analytics

arXiv:1911.01183 [math.AP]Abstract References Reviews Resources

Blow up of fractional Schrödinger equations on manifolds with nonnegative Ricci curvature

Published 2019-11-04Version 1

In this paper, the well-posedness of Cauchy's problem of fractional Schr\"odinger equations with a power type nonlinearity on manifolds with nonnegative Ricci curvature is studied. Under suitable volume conditions, the smooth solution will blow up in finite time no matter how small the initial data is, which follows from a new weight function and ODE inequalities. Moreover, the upper-bound of the lifespan can be estimated.

Comments: 10pages. Welcome all comments

Categories: math.AP

Subjects: 35A01

Keywords: nonnegative ricci curvature, fractional schrödinger equations, power type nonlinearity, ode inequalities, cauchys problem

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