Weighted Strichartz estimates with angular regularity and their applications

@inproceedings{Fang2008WeightedSE,
  title={Weighted Strichartz estimates with angular regularity and their applications},
  author={Daoyuan Fang and Chengbo Wang},
  year={2008}
}
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… 

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References

SHOWING 1-10 OF 49 REFERENCES

Angular Regularity and Strichartz Estimates for the Wave Equation

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect

A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions

Weighted Strichartz estimates with homogeneous weights with critical exponents are proved for the wave equation without a support restriction on the forcing term. The method of proof is based on

Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation

The aim of this article is twofold. First we consider the wave equation in the hyperbolic space HI and obtain the counterparts of the Strichartz type estimates in this context. Next we examine the

On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles

We establish the Strauss conjecture concerning small-data global existence for nonlinear wave equations, in the setting of exterior domains to compact obstacles, for space dimensions n = 3 and 4. The

Endpoint Strichartz estimates

<abstract abstract-type="TeX"><p>We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension <i>n</i> ≥ 4) and the

Sobolev inequalities with symmetry

In this paper, we derive some Sobolev inequalities for radially symmetric functions in Ḣs with 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space . These results are

Regularity of solutions to the free Schrödinger equation with radial initial data

We derive weighted smoothing inequalities for solutions of the free Schrödinger equation. As an application, we give a new proof of the endpoint Strichartz estimates in the radial case. We also

On the weighted estimate of the solution associated with the Schrödinger equation

Let u(x, t) be the solution of the Schrodinger equation with initial data f in the Sobolev space H −1+a/2 (R n ) with a>1. This paper shows that the weighted inequality ∫ Rn ∫ R |u(x, t)| 2 dt(1+|x|)