# The global well-posedness and scattering for the 5-dimensional defocusing conformal invariant NLW with radial initial data in a critical Besov space

@article{Miao2018TheGW, title={The global well-posedness and scattering for the 5-dimensional defocusing conformal invariant NLW with radial initial data in a critical Besov space}, author={Changxing Miao and Jianwei Yang and Tengfei Zhao}, journal={arXiv: Analysis of PDEs}, year={2018} }

In this paper, we obtain the global well-posedness and scattering for the radial solution to the defocusing conformal invariant nonlinear wave equation with initial data in the critical Besov space $\dot{B}^3_{1,1}\times\dot{B}^2_{1,1}(\mathbb{R}^5)$. This is the five dimensional analogue of \cite{dodson-2016}, which is the first result on the global well-posedness and scattering of the energy subcritical nonlinear wave equation without the uniform boundedness assumption on the critical Sobolev…

#### 2 Citations

Scattering theory for subcritical wave equation with inverse square potential.

- Physics, Mathematics
- 2020

We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method of [37], [38] and [41], we establish…

Scattering for the radial defocusing cubic nonlinear wave equation with initial data in the critical Sobolev space

- MathematicsDuke Mathematical Journal
- 2021

#### References

SHOWING 1-10 OF 34 REFERENCES

Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case

- Mathematics
- 2006

We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1 is smaller than that of the standing wave…

Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation

- Mathematics
- 2006

We study the energy-critical focusing non-linear wave equation, with data in the energy space, in dimensions 3, 4 and 5. We prove that for Cauchy data of energy smaller than the one of the static…

Scattering for radial energy-subcritical wave equations

- Mathematics
- 2016

In this paper, we study the focusing and defocusing energy--subcritical, nonlinear wave equation in $\mathbb{R}^{1+d}$ with radial initial data for $d = 4,5$. We prove that if a solution remains…

Scattering for radial energy-subcritical wave equations in dimensions 4 and 5

- Mathematics
- 2017

ABSTRACT In this paper, we consider the focusing and defocusing energy-subcritical, nonlinear wave equation in ℝ1+d with radial initial data for d = 4,5. We prove that if a solution remains bounded…

The defocusing energy-supercritical nonlinear wave equation in three space dimensions

- Mathematics
- 2010

We consider the defocusing nonlinear wave equation $u_{tt}-\Delta u + |u|^p u=0$ in the energy-supercritical regime p>4. For even values of the power p, we show that blowup (or failure to scatter)…

Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation

- Mathematics
- 1991

Abstract We study the long-time behavior of small solutions of the initial-value problem for the generalized Korteweg-de Vries equation ∂ t u + ∂ x 3 u + ∂ x F(u) = 0 (gKdV) u(x, 0) = g(x) . For the…

Lectures on Non-Linear Wave Equations

- Mathematics
- 2008

This much-anticipated revised second edition of Christopher Sogge's 1995 work provides a self-contained account of the basic facts concerning the linear wave equation and the methods from harmonic…

Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space

- Mathematics, PhysicsAnalysis & PDE
- 2019

In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in a slightly supercritical Sobolev space, and a weighted Sobolev space.

On Existence and Scattering with Minimal Regularity for Semilinear Wave Equations

- Mathematics
- 1995

Abstract We prove existence and scattering results for semilinear wave equations with low regularity data. We also determine the minimal regularity that is needed to ensure local existence and…

The global Cauchy problem for the non linear Klein-Gordon equation-II

- Mathematics
- 1986

Abstract We study the Cauchy problem for a class of non linear Klein-Gordon equations of the type φ .. − Δ φ + f ( φ ) = 0 by a contraction method. We prove the existence and uniqueness of strongly…