Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations
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We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain the full radial Strichartz estimates up to some endpoints for the Schrödinger equation. Using these estimates, we obtain some new results related to nonlinear problems, including small data scattering and large data LWP for the nonlinear Schrödinger and wave equations with radial critical initial data and the well-posedness theory for the fractional order Schrödinger equation in the radial case.
KeywordsDispersive Equation Nonlinear Wave Equation Critical Regularity Strichartz Estimate Radial Case
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- M. Christ, J. Colliander, and T. Tao, Ill-posedness for nonlinear Schrödinger and wave equations, arxiv:math/0311048[math.AP].Google Scholar
- M. Christ and A. Kiselev, Maximal functions associated to filtrations, J. Funct. Anal. 179 (2001), 406–425.Google Scholar
- R. Killip and M. Visan, Nonlinear Schrödinger equations at critical regularity, Evolution Equations, Amer. Math. Soc., Providence, RI, 2013, pp. 325–437.Google Scholar
- J. Sterbenz, Angular regularity and Strichartz estimates for the wave equation, with an appendix by Igor Rodnianski, Int. Math. Res. Not. 2005, 187–231.Google Scholar