On inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications
Chu-Hee Cho Youngwoo Koh Ihyeok Seo
Discrete & Continuous Dynamical Systems - A 2016, 36(4): 1905-1926 doi: 10.3934/dcds.2016.36.1905
In this paper we obtain some new inhomogeneous Strichartz estimates for the fractional Schrödinger equation in the radial case. Then we apply them to the well-posedness theory for the equation $i\partial_{t}u+|\nabla|^{\alpha}u=V(x,t)u$, $1<\alpha<2$, with radial $\dot{H}^\gamma$ initial data below $L^2$ and radial potentials $V\in L_t^rL_x^w$ under the scaling-critical range $\alpha/r+n/w=\alpha$.
keywords: Strichartz estimates well-posedness Schrödinger equations.

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