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SubmittedOpen Access (License Unspecified), Open
Journal article
ASYMPTOTIC STABILITY OF ASCENDING SOLITARY MAGMA WAVES
SIAM journal on mathematical analysis, v 40(4), pp 1337-1391
01 Jan 2008
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to evolving material parameters, modeling partially molten rock, magma, in the Earth's interior. Solitary waves are also found here, but the equations lack useful mathematical structures such as an inverse scattering transform or even a variational formulation. A common question in all of these applications is whether or not these structures are stable to perturbation. We prove that the solitary waves in this earth science setting are asymptotically stable and accomplish this without any preexisting Lyapunov stability. This holds true for a family of equations, extending beyond the physical parameter space. Furthermore, this extends existing results on well-posedness to data in a neighborhood of the solitary waves.
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Details
- Title
- ASYMPTOTIC STABILITY OF ASCENDING SOLITARY MAGMA WAVES
- Creators
- Gideon Simpson - Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USAMichael I. Weinstein - Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA
- Publication Details
- SIAM journal on mathematical analysis, v 40(4), pp 1337-1391
- Publisher
- Siam Publications
- Number of pages
- 55
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000263103500002
- Scopus ID
- 2-s2.0-67749103744
- Other Identifier
- 991019296804204721
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- Web of Science research areas
- Mathematics, Applied