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A note on the Euler–Voigt system in a 3D bounded domain: Propagation of singularities and absence of the boundary layer

1 Dipartimento di Matematica, Università di Pisa, Pisa, I56127, Italy
2 Sezione Matematica (DICATAM), Università degli Studi di Brescia, Brescia, I25133, Italy, Davide Catania

Topical Section: Mathematical Analysis in Fluid Dynamics

We consider the Euler–Voigt equations in a smooth bounded domain as an approximation for the 3D Euler equations. We show that the solutions of the Voigt equations are global, do not smooth out the data, and converge to the solutions of the Euler equations. For these reasons they represent a good model, also for computations of turbulent flows.
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Keywords model; Euler equations; smooth solutions; boundary layers; turbulence

Citation: Luigi C. Berselli, Davide Catania. A note on the Euler–Voigt system in a 3D bounded domain: Propagation of singularities and absence of the boundary layer. AIMS Mathematics, 2019, 4(1): 1-11. doi: 10.3934/Math.2019.1.1


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