Global Existence for General Systems of Isentropic Gas Dynamics via a Weighted Pressure Perturbation Approach
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915744025935872 |
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| author | Chen, Kewang |
| author_facet | Chen, Kewang |
| contents | We establish the global existence of weak entropy solutions for 1D isentropic gas dynamics with general pressure laws ($γ> 1$). To address vacuum degeneracy, we introduce a novel structural regularization via a "Synchronized Dual Translation" strategy. This approach offers a distinct advantage over the flux-modification method of Lu (2007): while Lu's method induces a structural mismatch requiring restrictive constraints on $P'''$ to control regularization artifacts, our construction preserves structural isomorphism with the standard Euler equations. Consequently, the approximate entropies satisfy a homogeneous Generalized Euler-Poisson-Darboux equation. This allows us to prove strong convergence under natural asymptotic assumptions, effectively eliminating the need for the technical higher-order derivative constraints required in prior works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08157 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Existence for General Systems of Isentropic Gas Dynamics via a Weighted Pressure Perturbation Approach Chen, Kewang Analysis of PDEs Mathematical Physics 35L65, 35L45, 35Q31, 76N10 We establish the global existence of weak entropy solutions for 1D isentropic gas dynamics with general pressure laws ($γ> 1$). To address vacuum degeneracy, we introduce a novel structural regularization via a "Synchronized Dual Translation" strategy. This approach offers a distinct advantage over the flux-modification method of Lu (2007): while Lu's method induces a structural mismatch requiring restrictive constraints on $P'''$ to control regularization artifacts, our construction preserves structural isomorphism with the standard Euler equations. Consequently, the approximate entropies satisfy a homogeneous Generalized Euler-Poisson-Darboux equation. This allows us to prove strong convergence under natural asymptotic assumptions, effectively eliminating the need for the technical higher-order derivative constraints required in prior works. |
| title | Global Existence for General Systems of Isentropic Gas Dynamics via a Weighted Pressure Perturbation Approach |
| topic | Analysis of PDEs Mathematical Physics 35L65, 35L45, 35Q31, 76N10 |
| url | https://arxiv.org/abs/2601.08157 |