Well-posedness for rough solutions of the 3D compressible Euler equations
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866918322161844224 |
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| author | Andersson, Lars Zhang, Huali |
| author_facet | Andersson, Lars Zhang, Huali |
| contents | In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity $(\mathbf{v}_0, ρ_0, \mathbf{w}_0) \in H^{2+} \times H^{2+} \times H^{2}$, improving on the regularity conditions of \cite{WQEuler}. The continuous dependence on initial data for rough solutions of the compressible Euler system is new, even with the same regularity conditions as in \cite{WQEuler}. In addition, we prove new local well-posedness results for the 3D compressible Euler system with entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10132 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Well-posedness for rough solutions of the 3D compressible Euler equations Andersson, Lars Zhang, Huali Analysis of PDEs Primary 76N10, 35R05, 35L60, 35Q35 In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity $(\mathbf{v}_0, ρ_0, \mathbf{w}_0) \in H^{2+} \times H^{2+} \times H^{2}$, improving on the regularity conditions of \cite{WQEuler}. The continuous dependence on initial data for rough solutions of the compressible Euler system is new, even with the same regularity conditions as in \cite{WQEuler}. In addition, we prove new local well-posedness results for the 3D compressible Euler system with entropy. |
| title | Well-posedness for rough solutions of the 3D compressible Euler equations |
| topic | Analysis of PDEs Primary 76N10, 35R05, 35L60, 35Q35 |
| url | https://arxiv.org/abs/2208.10132 |