Compressible fluids and active potentials
Constantin, Peter1 ; Drivas, Theodore D.1 ; Nguyen, Huy Q.1 ; Pasqualotto, Federico1, 2
1 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States of America
2 DPMMS, University of Cambridge, Cambridge CB3 0WA, United Kingdom
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 1, pp. 145-180.
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We consider a class of one dimensional compressible systems with degenerate diffusion coefficients. We establish the fact that the solutions remain smooth as long as the diffusion coefficients do not vanish, and give local and global existence results. The models include the barotropic compressible Navier-Stokes equations, shallow water systems and the lubrication approximation of slender jets. In all these models the momentum equation is forced by the gradient of a solution-dependent potential: the active potential. The method of proof uses the Bresch-Desjardins entropy and the analysis of the evolution of the active potential.

DOI : 10.1016/j.anihpc.2019.04.001
Classification : 76N10, 35Q30, 35Q35
Mots-clés : Compressible flow, Shallow water, Slender jet, Global existence
Constantin, Peter 1 ; Drivas, Theodore D. 1 ; Nguyen, Huy Q. 1 ; Pasqualotto, Federico 1, 2

1 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States of America
2 DPMMS, University of Cambridge, Cambridge CB3 0WA, United Kingdom 
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Constantin, Peter; Drivas, Theodore D.; Nguyen, Huy Q.; Pasqualotto, Federico. Compressible fluids and active potentials. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 1, pp. 145-180. doi : 10.1016/j.anihpc.2019.04.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2019.04.001/

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