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On blowup for the
supercritical quadratic wave equation
Elek Csobo, Irfan Glogić and Birgit Schörkhuber |
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Vol. 17 (2024), No. 2, 617–680
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Abstract |
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We study singularity formation for the quadratic wave equation in the energy supercritical case, i.e., for . We find in closed form a new, nontrivial, radial, self-similar blow-up solution which exists for all . For , we study the stability of without any symmetry assumptions on the initial data and show that there is a family of perturbations which lead to blowup via . In similarity coordinates, this family represents a codimension-1 Lipschitz manifold modulo translation symmetries. The stability analysis relies on delicate spectral analysis for a non-self-adjoint operator. In addition, in and , we prove nonradial stability of the well-known ODE blow-up solution. Also, for the first time we establish persistence of regularity for the wave equation in similarity coordinates. |
Keywords
nonlinear wave equation, supercritical, blowup, singularity
formation, self-similar solution, stability
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Mathematical Subject Classification
Primary: 35B44
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Milestones
Received: 8 October 2021
Accepted: 11 July 2022
Published: 6 March 2024
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Authors |
| Elek Csobo | |
| Universität Innsbruck Institut für Mathematik Technikerstraße 13 6020 Innsbruck Austria |
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| Irfan Glogić | |
| Faculty of Mathematics University of Vienna Vienna Austria |
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| Birgit Schörkhuber | |
| Universität Innsbruck Institut für Mathematik Technikerstraße 13 6020 Innsbruck Austria |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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