Global well-posedness and stability of the inhomogeneous kinetic wave equation near vacuum
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911769063063552 |
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| author | Ampatzoglou, Ioakeim |
| author_facet | Ampatzoglou, Ioakeim |
| contents | In this paper, we prove global in time existence, uniqueness and stability of mild solutions near vacuum for the 4-wave inhomogeneous kinetic wave equation, for Laplacian dispersion relation in dimension $d=2,3$. We also show that for non-negative initial data, the solution remains non-negative. This is achieved by connecting the inhomogeneous kinetic wave equation to the cubic part of a quantum Boltzmann-type equation with moderately hard potential and no collisional averaging. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2207_08315 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and stability of the inhomogeneous kinetic wave equation near vacuum Ampatzoglou, Ioakeim Analysis of PDEs Mathematical Physics In this paper, we prove global in time existence, uniqueness and stability of mild solutions near vacuum for the 4-wave inhomogeneous kinetic wave equation, for Laplacian dispersion relation in dimension $d=2,3$. We also show that for non-negative initial data, the solution remains non-negative. This is achieved by connecting the inhomogeneous kinetic wave equation to the cubic part of a quantum Boltzmann-type equation with moderately hard potential and no collisional averaging. |
| title | Global well-posedness and stability of the inhomogeneous kinetic wave equation near vacuum |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2207.08315 |