Low regularity solutions of two-dimensional compressible Euler equations with dynamic vorticity
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arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866915301799493632 |
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| author | Zhang, Huali |
| author_facet | Zhang, Huali |
| contents | By establishing a sharp Strichartz estimate for the velocity and density, we prove the local well-posedness of solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial velocity, density, and specific vorticity $(\bv_0, ρ_0, \varpi_0) \in H^{s}(\mathbb{R}^2)\times H^{s}(\mathbb{R}^2) \times H^2(\mathbb{R}^2), s>\frac{7}{4}$. Our strategy relies on Smith-Tataru's work \cite{ST} for quasi-linear wave equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_01060 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Low regularity solutions of two-dimensional compressible Euler equations with dynamic vorticity Zhang, Huali Analysis of PDEs Primary 76N10, 35R05, 35L60 By establishing a sharp Strichartz estimate for the velocity and density, we prove the local well-posedness of solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial velocity, density, and specific vorticity $(\bv_0, ρ_0, \varpi_0) \in H^{s}(\mathbb{R}^2)\times H^{s}(\mathbb{R}^2) \times H^2(\mathbb{R}^2), s>\frac{7}{4}$. Our strategy relies on Smith-Tataru's work \cite{ST} for quasi-linear wave equations. |
| title | Low regularity solutions of two-dimensional compressible Euler equations with dynamic vorticity |
| topic | Analysis of PDEs Primary 76N10, 35R05, 35L60 |
| url | https://arxiv.org/abs/2012.01060 |