Vol. 15, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 7, 1617–1859
Issue 6, 1375–1616
Issue 5, 1131–1373
Issue 4, 891–1130
Issue 3, 567–890
Issue 2, 273–566
Issue 1, 1–272

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
On the global behaviors for defocusing semilinear wave equations in $\mathbb{R}^{1+2}$

Dongyi Wei and Shiwu Yang

Vol. 15 (2022), No. 1, 245–272
Abstract

We study the asymptotic decay properties for defocusing semilinear wave equations in 1+2 with pure power nonlinearity. By applying new vector fields to the null hyperplane, we derive improved time decay of the potential energy, with a consequence that the solution scatters both in the critical Sobolev space and energy space for all p > 1 + 8. Moreover, combined with Brezis–Gallouet–Wainger-type of logarithmic Sobolev embedding, we show that the solution decays pointwise with sharp rate t12 when p > 11 3 and with rate t(p1)8+𝜖 for all 1 < p 11 3 . This in particular implies that the solution scatters in energy space when p > 25 1.

Keywords
asymptotic behavior, defocusing semilinear wave equation, energy subcritical
Mathematical Subject Classification
Primary: 35L05
Milestones
Received: 4 March 2020
Revised: 9 March 2020
Accepted: 15 September 2020
Published: 16 March 2022
Authors
Dongyi Wei
School of Mathematical Sciences
Peking University
Beijing
China
Shiwu Yang
Beijing International Center for Mathematical Research
Peking University
Beijing
China