Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in <(H)over dot> x <(H)over dot>s-1, s > 1/2

被引：2

作者：

Dodson, Benjamin ^{[1
]}

机构：

[1] Johns Hopkins Univ, 404 Krieger Hall,3400 N Charles St, Baltimore, MD 21218 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2019年 / 2019卷 / 21期

基金：

美国国家科学基金会;

关键词：

SCHRODINGER-EQUATION; LOCAL EXISTENCE; ROUGH SOLUTIONS; SCATTERING; REGULARITY;

D O I：

10.1093/imrn/rnx323

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is <(H)over dot>(1/2) x <(H)over dot>(-1/2) . We show that if the initial data is radial and lies in (<(H)over dot>(s) x <(H)over dot>(s-1)) boolean AND (<(H)over dot>(1/2) x <(H)over dot>(-1/2)) for some , then the cubic initial value problem is globally well-posed. The proof utilizes the I-method, long time Strichartz estimates, and local energy decay. This method is quite similar to the method used in [11].

引用

页码：6797 / 6817

页数：21

共 50 条

[41] Ab initio potential-energy surfaces for the (X)over-tilde 2B1, (A)over-tilde 2A1, and (B)over-tilde 2B2 states of the H2S+ molecular ion
Hirst, DM
JOURNAL OF CHEMICAL PHYSICS, 2003, 118 (20): : 9175 - 9184
[42] H2CS-C6H6 cluster effects in the S-T conversion dynamics of H2CS excited to individual rotational levels of the ((X)over-tilde1A1←(A)over-tilde1A2)000 electron-vibrational transition:: OD EPR studies
Makarov, VI
Khmelinskii, IV
CHEMICAL PHYSICS, 2004, 306 (1-3) : 13 - 24
[43] Wave packet quantum dynamics of C(3P) + H2(X1Σg+) → H(2S) + CH(2Π) reaction based on new CH2((x)over-tilde3A") surface
Zhao Wen-Li
Wang Yong-Gang
Zhang Lu-Lu
Yue Da-Guang
Meng Qing-Tian
ACTA PHYSICA SINICA, 2020, 69 (08)
[44] Determination of the Rate Constants for the Radical-Radical Reactions NH2((X)over-tilde2B1) + NH(X3Σ-) and NH2((X)over-tilde2B1) + H(2S) at 293 K
Bahng, Mi-Kyung
Macdonald, R. Glen
JOURNAL OF PHYSICAL CHEMISTRY A, 2009, 113 (11): : 2415 - 2423
[45] A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl(2P)+H2→HCl(X)over-tilde1Σg+)+H(2S) reaction
Ghosal, S
Mahapatra, S
JOURNAL OF CHEMICAL PHYSICS, 2004, 121 (12): : 5740 - 5753
[46] Energy-dependent stereodynamics for the H(2S)+NH(X3(Σ)over-bar)→H2(X1Σg+)+N(4S) reaction on the improved ZH potential energy surface
Yao, Cui-Xia
Zhao, Guang-Jiu
CANADIAN JOURNAL OF CHEMISTRY, 2013, 91 (06) : 387 - 391
[47] Global Well-Posedness of a Two–Component b–Family Equations in Hs-1,p(R)×Hs,p(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{s-1,p}({\mathbb {R}})\times H^{s,p}({\mathbb {R}})$$\end{document}
Lijun Du
Xinglong Wu
Journal of Mathematical Fluid Mechanics, 2022, 24 (4)
[48] Ab initio MO studies on the photodissociation of the methoxy family CX(3)Y (X=H,F; Y=O,S) from the (A)over-tilda(2)A(1) state
Cui, Q
Morokuma, K
CHEMICAL PHYSICS LETTERS, 1996, 263 (1-2) : 54 - 62
[49] State-to-state quantum dynamics of the H(2S) + O2((a)over-tilde1Δg) → O(3P) + OH((X)over-tilde2 Π) reaction on the first excited state of HO2((A)over-tilde2A′)
Ma, Jianyi
Guo, Hua
Xie, Changjian
Li, Anyang
Xie, Daiqian
PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 2011, 13 (18) : 8407 - 8413
[50] Photocatalytic H2 evolution under visible-light irradiation over band-structure-controlled (CuIn)xZn2(1-x)S2 solid solutions
Tsuji, I
Kato, H
Kobayashi, H
Kudo, A
JOURNAL OF PHYSICAL CHEMISTRY B, 2005, 109 (15): : 7323 - 7329

← 1 2 3 4 5 →