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On the global
behaviors for defocusing semilinear wave equations in
$\mathbb{R}^{1+2}$
Dongyi Wei and Shiwu Yang |
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Vol. 15 (2022), No. 1, 245–272
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Abstract |
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We study the asymptotic decay properties for defocusing semilinear wave equations in 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 . Moreover, combined with Brezis–Gallouet–Wainger-type of logarithmic Sobolev embedding, we show that the solution decays pointwise with sharp rate when and with rate for all . This in particular implies that the solution scatters in energy space when . |
Keywords
asymptotic behavior, defocusing semilinear wave equation,
energy subcritical
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Mathematical Subject Classification
Primary: 35L05
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Milestones
Received: 4 March 2020
Revised: 9 March 2020
Accepted: 15 September 2020
Published: 16 March 2022
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Authors |
| Dongyi Wei | |
| School of Mathematical
Sciences Peking University Beijing China |
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| Shiwu Yang | |
| Beijing International Center for
Mathematical Research Peking University Beijing China |
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