ON FRACTIONAL SCHRODINGER EQUATIONS IN SOBOLEV SPACES

초록

Let sigma is an element of (0, 1) with sigma not equal 1/2. We investigate the fractional nonlinear Schrodinger equation in R-d: i partial derivative(t)u + (-Delta)(sigma)u + mu vertical bar mu vertical bar(p-1)u = 0, u(0) = u(0) is an element of H-s, where (-Delta)(sigma) is the Fourier multiplier of symbol vertical bar xi vertical bar(2 sigma), and mu = +/- 1. This model has been introduced by Laskin in quantum physics [23]. We establish local well-posedness and ill-posedness in Sobolev spaces for power-type nonlinearities.

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