The Equations of Extended Magnetohydrodynamics
Uložené v:
| Názov: | The Equations of Extended Magnetohydrodynamics |
|---|---|
| Autori: | Besse, Nicolas, Cheverry, Christophe |
| Prispievatelia: | Cheverry, Christophe |
| Zdroj: | SIAM Journal on Mathematical Analysis. 57:4519-4555 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Society for Industrial & Applied Mathematics (SIAM), 2025. |
| Rok vydania: | 2025 |
| Predmety: | Hyperbolic-parabolic symmetric systems of conservation laws Initial value problem for nonlinear systems of PDEs Partially elliptic systems Compressible and incompressible fluid mechanics Plasma physics Hall, Inertial and Extended Magnetohydrodynamics Pseudo-differential operators Weyl quantization, Weyl quantization, 7. Clean energy, Plasma physics, Mathematics - Analysis of PDEs, Pseudo-differential operators, Hall, FOS: Mathematics, Inertial and Extended Magnetohydrodynamics, Hyperbolic-parabolic symmetric systems of conservation laws, Compressible and incompressible fluid mechanics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Initial value problem for nonlinear systems of PDEs, Partially elliptic systems, Analysis of PDEs (math.AP) |
| Popis: | Extended magnetohydrodynamics (XMHD) is a fluid plasma model generalizing ideal MHD by taking into account the impact of Hall drift effects and the influence of electron inertial effects. XMHD has a Hamiltonian structure which has received over the past ten years a great deal of attention among physicists, and which is embodied by a non canonical Poisson algebra on an infinite-dimensional phase space. XMHD can alternatively be formulated as a nonlinear evolution equation. Our aim here is to investigate the corresponding Cauchy problem. We consider both incompressible and compressible versions of XMHD with, in the latter case, some additional bulk (fluid) viscosity. In this context, we show that XMHD can be recast as a well-posed symmetric hyperbolic-parabolic system implying pseudo-differential operators of order zero acting as coefficients and source terms. Along these lines, we can solve locally in time the associated initial value problems, with moreover a minimal Sobolev regularity. We also explain the emergence and propagation of inertial waves. |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 1095-7154 0036-1410 |
| DOI: | 10.1137/24m1702532 |
| DOI: | 10.48550/arxiv.2406.17356 |
| Prístupová URL adresa: | http://arxiv.org/abs/2406.17356 https://hal.science/hal-04622238v1 https://doi.org/10.1137/24m1702532 https://hal.science/hal-04622238v1/document |
| Rights: | arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....4da69b52c1c9e2c22f52b008bf5df7b2 |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | Extended magnetohydrodynamics (XMHD) is a fluid plasma model generalizing ideal MHD by taking into account the impact of Hall drift effects and the influence of electron inertial effects. XMHD has a Hamiltonian structure which has received over the past ten years a great deal of attention among physicists, and which is embodied by a non canonical Poisson algebra on an infinite-dimensional phase space. XMHD can alternatively be formulated as a nonlinear evolution equation. Our aim here is to investigate the corresponding Cauchy problem. We consider both incompressible and compressible versions of XMHD with, in the latter case, some additional bulk (fluid) viscosity. In this context, we show that XMHD can be recast as a well-posed symmetric hyperbolic-parabolic system implying pseudo-differential operators of order zero acting as coefficients and source terms. Along these lines, we can solve locally in time the associated initial value problems, with moreover a minimal Sobolev regularity. We also explain the emergence and propagation of inertial waves. |
|---|---|
| ISSN: | 10957154 00361410 |
| DOI: | 10.1137/24m1702532 |