Global existence of Euler-Korteweg equations with the non-monotone pressure
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917926302384128 |
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| author | Song, Zihao |
| author_facet | Song, Zihao |
| contents | We are concerned with the global solution of the compressible Euler-Korteweg equations in $\mathbb{R}^{3}$. In the case of zero sound speed $P'(ρ^{\ast})=0$, it is found that the perturbation problem of irrotational fluids could be reformulated into a quasi-linear Schr$\ddot{o}$dinger equation. Based on techniques of dispersive estimates and methods of normal form, we construct a class of global scattering solutions for 3D case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06511 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global existence of Euler-Korteweg equations with the non-monotone pressure Song, Zihao Analysis of PDEs 76N10, 35D05, 35Q31 We are concerned with the global solution of the compressible Euler-Korteweg equations in $\mathbb{R}^{3}$. In the case of zero sound speed $P'(ρ^{\ast})=0$, it is found that the perturbation problem of irrotational fluids could be reformulated into a quasi-linear Schr$\ddot{o}$dinger equation. Based on techniques of dispersive estimates and methods of normal form, we construct a class of global scattering solutions for 3D case. |
| title | Global existence of Euler-Korteweg equations with the non-monotone pressure |
| topic | Analysis of PDEs 76N10, 35D05, 35Q31 |
| url | https://arxiv.org/abs/2307.06511 |