Derivation and well-posedness for asymptotic models of cold plasmas
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917423723053056 |
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| author | Alonso-Orán, Diego Durán, Ángel Granero-Belinchón, Rafael |
| author_facet | Alonso-Orán, Diego Durán, Ángel Granero-Belinchón, Rafael |
| contents | In this paper we derive three new asymptotic models for an hyperbolic-hyperbolicelliptic system of PDEs describing the motion of a collision-free plasma in a magnetic field. The first of these models takes the form of a non-linear and non-local Boussinesq system (for the ionic density and velocity) while the second is a non-local wave equation (for the ionic density). Moreover, we derive a unidirectional asymptotic model of the later which is closely related to the well-known Fornberg-Whitham equation. We also provide the well-posedness of these asymptotic models in Sobolev spaces. To conclude, we demonstrate the existence of a class of initial data which exhibit wave breaking for the unidirectional model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_13922 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Derivation and well-posedness for asymptotic models of cold plasmas Alonso-Orán, Diego Durán, Ángel Granero-Belinchón, Rafael Analysis of PDEs Mathematical Physics Fluid Dynamics In this paper we derive three new asymptotic models for an hyperbolic-hyperbolicelliptic system of PDEs describing the motion of a collision-free plasma in a magnetic field. The first of these models takes the form of a non-linear and non-local Boussinesq system (for the ionic density and velocity) while the second is a non-local wave equation (for the ionic density). Moreover, we derive a unidirectional asymptotic model of the later which is closely related to the well-known Fornberg-Whitham equation. We also provide the well-posedness of these asymptotic models in Sobolev spaces. To conclude, we demonstrate the existence of a class of initial data which exhibit wave breaking for the unidirectional model. |
| title | Derivation and well-posedness for asymptotic models of cold plasmas |
| topic | Analysis of PDEs Mathematical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2305.13922 |