On stability of solitons for 3D Maxwell-Lorentz equations with spinning particle
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| Format: | Preprint |
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2023
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| author | Komech, Alexander Kopylova, Elena |
| author_facet | Komech, Alexander Kopylova, Elena |
| contents | We consider stability of solitons of 3D Maxwell--Lorentz system with extended charged spinning particle.The solitons are solutions which correspond to a particle moving with a constant velocity $v\in\R^3$ with $|v|<1$ and rotating with a constant angular velocity $ω\in R^3$.
Our main results are the orbital stability of moving solitons with $ω=0$ and a {\it linear} orbital stability of rotating solitons with $v=0$.
The Hamilton--Poisson structure of the Maxwell--Lorentz system is degenerate and admits the Casimir invariants. We construct the Lyapunov function as a linear combination of the Hamiltonian with a suitable Casimir invariant. The key point is a lower bound for this function. The proof of the bound in the case $\om\ne 0$ relies on angular momentum conservation and suitable spectral arguments including the Heinz inequality and closed graph theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00508 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On stability of solitons for 3D Maxwell-Lorentz equations with spinning particle Komech, Alexander Kopylova, Elena Mathematical Physics 35Q61, 37K06, 37K40, 53D17, 70S05, 70G65, 70G45 We consider stability of solitons of 3D Maxwell--Lorentz system with extended charged spinning particle.The solitons are solutions which correspond to a particle moving with a constant velocity $v\in\R^3$ with $|v|<1$ and rotating with a constant angular velocity $ω\in R^3$. Our main results are the orbital stability of moving solitons with $ω=0$ and a {\it linear} orbital stability of rotating solitons with $v=0$. The Hamilton--Poisson structure of the Maxwell--Lorentz system is degenerate and admits the Casimir invariants. We construct the Lyapunov function as a linear combination of the Hamiltonian with a suitable Casimir invariant. The key point is a lower bound for this function. The proof of the bound in the case $\om\ne 0$ relies on angular momentum conservation and suitable spectral arguments including the Heinz inequality and closed graph theorem. |
| title | On stability of solitons for 3D Maxwell-Lorentz equations with spinning particle |
| topic | Mathematical Physics 35Q61, 37K06, 37K40, 53D17, 70S05, 70G65, 70G45 |
| url | https://arxiv.org/abs/2306.00508 |