# 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…

## 77 Citations

### Generalized and weighted Strichartz estimates

- Mathematics
- 2012

In this paper, we explore the relations between different kinds of Strichartz estimates
and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted…

### Inequalities with angular integrability and applications

- Mathematics
- 2013

We prove an extension of the Stein-Weiss weighted estimates for fractional integrals, in the context of Lp spaces with different integrability properties in the radial and the angular direction. In…

### Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations

- Mathematics
- 2021

. In this paper we study the Cauchy problem for the inhomogeneous Hartree equation. Its well-posedness theory has been intensively studied in recent several years, but much less is understood…

### Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations

- Mathematics
- 2010

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…

### Sharp local well-posedness for quasilinear wave equations with spherical symmetry

- Mathematics
- 2020

In this paper, we prove a sharp local well-posedness result for spherically symmetric solutions to quasilinear wave equations with rough initial data, when the spatial dimension is three or higher.…

### Endpoint Strichartz estimates with angular integrability and some applications

- MathematicsJournal of Evolution Equations
- 2022

The endpoint Strichartz estimate ‖eit∆f‖L2tL∞x . ‖f‖L2 is known to be false in two space dimensions. Taking averages spherically on the polar coordinates x = ρω, ρ > 0, ω ∈ S, Tao showed a substitute…

### Almost Global Existence for Some Semilinear Wave Equations with Almost Critical Regularity

- Mathematics
- 2013

For any subcritical index of regularity s > 3/2, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the…

### An endpoint Strichartz estimate in spherical coordinates (Harmonic Analysis and Nonlinear Partial Differential Equations)

- Mathematics
- 2012

We study Strichartz estimates in spherical coordinates for dispersive equations which are defined by spherically symmetric pseudo‐differential operators. We extend the recent results in [7, 11] to…

## References

SHOWING 1-10 OF 49 REFERENCES

### Angular Regularity and Strichartz Estimates for the Wave Equation

- Mathematics
- 2004

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

- Mathematics
- 2005

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

- Mathematics
- 2000

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

- Mathematics
- 2008

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

- Mathematics
- 1998

<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

- Mathematics
- 2007

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

- Mathematics
- 2001

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

- Mathematics
- 1991

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|)…