Zero Mach Number Limit of the Compressible Primitive Equations: Well-Prepared Initial Data
Titi, Edriss S.
Archive for Rational Mechanics and Analysis
Springer Berlin Heidelberg
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Liu, X., & Titi, E. S. (2020). Zero Mach Number Limit of the Compressible Primitive Equations: Well-Prepared Initial Data. Archive for Rational Mechanics and Analysis, 238 (2), 705-747. https://doi.org/10.1007/s00205-020-01553-z
Funder: Einstein Stiftung Berlin; doi: http://dx.doi.org/10.13039/501100006188
Funder: John Simon Guggenheim Memorial Foundation; doi: http://dx.doi.org/10.13039/100005851
Abstract: This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are identified as the limiting equations. The convergence with well-prepared initial data (i.e., initial data without acoustic oscillations) is rigorously justified, and the convergence rate is shown to be of order O(ε), as ε→0+, where ε represents the Mach number. As a byproduct, we construct a class of global solutions to the compressible primitive equations, which are close to the incompressible flows.
External DOI: https://doi.org/10.1007/s00205-020-01553-z
This record's URL: https://www.repository.cam.ac.uk/handle/1810/324933