Weak and classical solutions to an asymptotic model for atmospheric flows
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914769184751616 |
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| author | Matioc, Bogdan-Vasile Roberti, Luigi |
| author_facet | Matioc, Bogdan-Vasile Roberti, Luigi |
| contents | In this paper we study a recently derived mathematical model for nonlinear propagation of waves in the atmosphere, for which we establish the local well-posedness in the setting of classical solutions. This is achieved by formulating the model as a quasilinear parabolic evolution problem in an appropriate functional analytic framework and by using abstract theory for such problems. Moreover, for $L_2$-initial data, we construct global weak solutions by employing a two-step approximation strategy based on a Galerkin scheme, where an equivalent formulation of the problem in terms of a new variable is used. Compared to the original model, the latter has the advantage that the $L_2$-norm is a Liapunov functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08985 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weak and classical solutions to an asymptotic model for atmospheric flows Matioc, Bogdan-Vasile Roberti, Luigi Analysis of PDEs 35D30, 35K59, 35Q86 In this paper we study a recently derived mathematical model for nonlinear propagation of waves in the atmosphere, for which we establish the local well-posedness in the setting of classical solutions. This is achieved by formulating the model as a quasilinear parabolic evolution problem in an appropriate functional analytic framework and by using abstract theory for such problems. Moreover, for $L_2$-initial data, we construct global weak solutions by employing a two-step approximation strategy based on a Galerkin scheme, where an equivalent formulation of the problem in terms of a new variable is used. Compared to the original model, the latter has the advantage that the $L_2$-norm is a Liapunov functional. |
| title | Weak and classical solutions to an asymptotic model for atmospheric flows |
| topic | Analysis of PDEs 35D30, 35K59, 35Q86 |
| url | https://arxiv.org/abs/2304.08985 |