Characteristics of drift effects arising from nonlinear symmetry of the quasi-geostrophic equation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915752236285952 |
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| author | Yamamoto, Masakazu |
| author_facet | Yamamoto, Masakazu |
| contents | This paper compares two similar diffusion equations that appear in meteorology. One is the quasi-geostrophic equation, and the other is the convection-diffusion equation. Both are two-dimensional bilinear equations, and the order of differentiation is the same. Naturally, their scales also coincide. However, the direction in which the nonlinear effects act differs: one acts along the isothermal surface, while the other acts along the temperature gradient in a specified direction. The main assertion quantifies this difference through the large-time behavior of their solutions. In particular, the nonlinear distortions in the asymptotic profiles of both equations are compared. In this context, the spatial symmetry of the first approximation plays a crucial role, but the solutions require no symmetry. As an appendix, the mixed problem of those models are studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10185 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characteristics of drift effects arising from nonlinear symmetry of the quasi-geostrophic equation Yamamoto, Masakazu Analysis of PDEs 35B05, 35B06, 35B40, 35C20, 35K55, 35Q35, 35Q79, 35Q86, 86A05 This paper compares two similar diffusion equations that appear in meteorology. One is the quasi-geostrophic equation, and the other is the convection-diffusion equation. Both are two-dimensional bilinear equations, and the order of differentiation is the same. Naturally, their scales also coincide. However, the direction in which the nonlinear effects act differs: one acts along the isothermal surface, while the other acts along the temperature gradient in a specified direction. The main assertion quantifies this difference through the large-time behavior of their solutions. In particular, the nonlinear distortions in the asymptotic profiles of both equations are compared. In this context, the spatial symmetry of the first approximation plays a crucial role, but the solutions require no symmetry. As an appendix, the mixed problem of those models are studied. |
| title | Characteristics of drift effects arising from nonlinear symmetry of the quasi-geostrophic equation |
| topic | Analysis of PDEs 35B05, 35B06, 35B40, 35C20, 35K55, 35Q35, 35Q79, 35Q86, 86A05 |
| url | https://arxiv.org/abs/2601.10185 |