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Global convergence to compressible full Navier-Stokes equations by approximation with Oldroyd-type constitutive laws

Abstract : We consider smooth solutions to a relaxed Euler system with Oldroyd-type constitutive laws. This system is derived from the one-dimensional compressible full Navier-Stokes equations for a Newtonian fluid by using the Cattaneo-Christov model and the Oldroyd-B model. In a neighborhood of equilibrium states, we construct an explicit symmetrizer and show that the system is symmetrizable hyperbolic with partial dissipation. Moreover, by establishing uniform estimates with respect to the relaxation times, we prove the uniform global existence of smooth solutions and the global-in-time convergence of the system towards the full Navier-Stokes equations.
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https://hal.uca.fr/hal-03660217
Contributor : Yue-Jun Peng Connect in order to contact the contributor
Submitted on : Thursday, May 5, 2022 - 4:10:07 PM
Last modification on : Saturday, May 7, 2022 - 3:35:07 AM

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Yue-Jun Peng, Liang Zhao. Global convergence to compressible full Navier-Stokes equations by approximation with Oldroyd-type constitutive laws. Journal of Mathematical Fluid Mechanics, Springer Verlag, 2022, 24 (2), pp.29. ⟨10.1007/s00021-022-00669-4⟩. ⟨hal-03660217⟩

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