Improved a priori bounds for thermal fluid equations
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- by Andrei Tarfulea PDF
- Trans. Amer. Math. Soc. 371 (2019), 2719-2737 Request permission
Abstract:
We consider two hydrodynamic model problems (one incompressible and one compressible) with three-dimensional fluid flow on the torus and temperature-dependent viscosity and conductivity. The ambient heat for the fluid is transported by the flow and fed by the local energy dissipation, modeling the transfer of kinetic energy into thermal energy through fluid friction. Both the viscosity and conductivity grow with the local temperature. We prove a strong a priori bound on the enstrophy of the velocity weighed against the temperature for initial data of arbitrary size, requiring only that the conductivity be proportionately larger than the viscosity (and, in the incompressible case, a bound on the temperature as a Muckenhoupt weight).References
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Additional Information
- Andrei Tarfulea
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois
- MR Author ID: 871723
- Email: atarfulea@math.uchicago.edu
- Received by editor(s): February 13, 2017
- Received by editor(s) in revised form: February 27, 2017, and January 3, 2018
- Published electronically: September 18, 2018
- Additional Notes: The author was partially supported by NSF grant DMS-1246999.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 2719-2737
- MSC (2010): Primary 76N10; Secondary 35A01, 35A23, 35Q35
- DOI: https://doi.org/10.1090/tran/7529
- MathSciNet review: 3896095