Smooth and stable Euler implosions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914524929458176 |
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| author | Chen, Jiajie Shkoller, Steve Vicol, Vlad |
| author_facet | Chen, Jiajie Shkoller, Steve Vicol, Vlad |
| contents | We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/spherically symmetric, and have explicit (closed-form) similarity exponents. We prove that the exact Euler solution corresponding to the ground state implosion profile is stable to radially symmetric perturbations, as a solution to the full nonlinear compressible Euler equations, modulo a one-dimensional compatibility condition on the initial data. For perturbations of the Euler solution corresponding to the ground state implosion profile of a monatomic or diatomic gas, that do not obey any symmetry assumptions, we provide a complete characterization of the set of initial data that yield nonlinear stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00808 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smooth and stable Euler implosions Chen, Jiajie Shkoller, Steve Vicol, Vlad Analysis of PDEs 35L67, 76L05, 76N10, We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/spherically symmetric, and have explicit (closed-form) similarity exponents. We prove that the exact Euler solution corresponding to the ground state implosion profile is stable to radially symmetric perturbations, as a solution to the full nonlinear compressible Euler equations, modulo a one-dimensional compatibility condition on the initial data. For perturbations of the Euler solution corresponding to the ground state implosion profile of a monatomic or diatomic gas, that do not obey any symmetry assumptions, we provide a complete characterization of the set of initial data that yield nonlinear stability. |
| title | Smooth and stable Euler implosions |
| topic | Analysis of PDEs 35L67, 76L05, 76N10, |
| url | https://arxiv.org/abs/2605.00808 |