dorsal/arxiv
View SchemaOn some recent results about inertial manifolds and kinematic dynamos
| Authors | Manuel Nunez |
|---|---|
| Categories | |
| ArXiv ID | physics/0503182 |
| URL | https://arxiv.org/abs/physics/0503182 |
Abstract
The conditions imposed in the paper ['Inertial manifolds and completeness of eigenmodes for unsteady magnetic dynamos', Physica D {\bf 194} (2004) 297-319] on the fluid velocity to guarantee the existence of inertial manifolds for the kinematic dynamo problem are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical kinematic dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.
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"abstract": "The conditions imposed in the paper [\u0027Inertial manifolds and completeness of\neigenmodes for unsteady magnetic dynamos\u0027, Physica D {\\bf 194} (2004) 297-319]\non the fluid velocity to guarantee the existence of inertial manifolds for the\nkinematic dynamo problem are too demanding, in the sense that they imply that\nall the solutions tend exponentially to zero. The inertial manifolds are\nmeaningful because they represent different decay rates, but the classical\nkinematic dynamos where the magnetic field is maintained or grows are not\ncovered by this approach, at least until more refined estimates are found.",
"arxiv_id": "physics/0503182",
"authors": [
"Manuel Nunez"
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"title": "On some recent results about inertial manifolds and kinematic dynamos",
"url": "https://arxiv.org/abs/physics/0503182"
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