Existence and uniqueness of small energy weak solution to multi-dimensional compressible Navier-Stokes equations with large external potential force

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Abstract

We study the 3-D compressible Navier-Stokes equations with an external potential force and a general non-decreasing pressure. We prove the global-in-time existence of weak solutions with small-energy initial data and with densities being non-negative and essentially bounded. A solution may have large oscillations and contain vacuum states. No smallness assumption is made on the external force nor the initial perturbation in L∞ for density. Initial velocity u₀ is taken to be bounded in Lq for some q > 6 and no further regularity assumption is imposed on u₀. Finally, we discuss the uniqueness of weak solutions. Copyright © 2016 AIP Publishing.
Original languageEnglish
Article number081513
JournalJournal of Mathematical Physics
Volume57
Issue number8
Early online dateAug 2016
DOIs
Publication statusPublished - 2016

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Compressible Navier-Stokes Equations
uniqueness
Navier-Stokes equation
Weak Solution
Existence and Uniqueness
Existence of Weak Solutions
Energy
regularity
3D
Vacuum
Uniqueness
Regularity
Non-negative
Oscillation
Perturbation
perturbation
vacuum
oscillations
energy

Citation

Cheung, K. L., & Suen, A. (2016, August). Existence and uniqueness of small energy weak solution to multi-dimensional compressible Navier-Stokes equations with large external potential force. Journal of Mathematical Physics, 57(8). Retrieved October 19, 2016, from http://dx.doi.org/10.1063/1.4960749