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Weighted Strichartz estimates with angular regularity and their applications
-
Daoyuan Fang
and
Chengbo Wang
Published/Copyright:
April 14, 2010
Abstract
In this paper, we establish an optimal dual version of trace estimate involving angular regularity. Based on this estimate, we get the generalized Morawetz estimates and weighted Strichartz estimates for the solutions to a large class of evolution equations, including the wave and Schrödinger equation. As applications, we prove the Strauss' conjecture with a kind of mild rough data for 2 ≤ n ≤ 4, and a result of global well-posedness with small data for some nonlinear Schrödinger equation with L2-subcritical nonlinearity.
Keywords.: Trace lemma; generalized Morawetz estimate; Strichartz estimate; wave equation; Schrödinger equation; angular regularity; Strauss' conjecture
Received: 2008-11-16
Revised: 2009-04-22
Published Online: 2010-04-14
Published in Print: 2011-January
© de Gruyter 2011
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Keywords for this article
Trace lemma;
generalized Morawetz estimate;
Strichartz estimate;
wave equation;
Schrödinger equation;
angular regularity;
Strauss' conjecture
Articles in the same Issue
- Semi-classical limits of the first eigenfunction and concentration on the recurrent sets of a dynamical system
- Ree geometries
- Centralisers of finite subgroups in soluble groups of type FPn
- Visibility and diameter maximization of convex bodies
- The Bergman kernel and mass equidistribution on the Siegel modular variety
- Lp boundedness for parabolic Schrödinger type operators with certain nonnegative potentials
- Weighted Strichartz estimates with angular regularity and their applications
- Classification of (1, 2)-Grassmann secant defective threefolds
