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تسجيل مستخدم جديدOn the high-low method for NLS on the hyperbolic space
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In this paper, we first prove that the cubic, defocusing nonlinear Schrodinger equation on the two dimensional hyperbolic space with radial initial data in $H^s(mathbb{H}^2)$ is globally well-posed and scatters when $s > frac{3}{4}$. Then we extend the result to nonlineraities of order $p>3$. The result is proved by extending the high-low method of Bourgain in the hyperbolic setting and by using a Morawetz type estimate proved by the first author and Ionescu.
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