The vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow

Comptes Rendus Mathematique

Volumn 350, Issue 15-16, 2012, Pages 757-760

  Bardos, Claude ^a   Titi, Edriss S ^b,c   Wiedemann, Emil ^d  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^d UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867335602     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2012.09.005     Document Type: Article

References (11)

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2. Bardos Claude, Titi Edriss S. Loss of smoothness and energy conserving rough weak solutions for the 3D Euler equations. Discrete Contin. Dyn. Syst. Ser. 2010, 3(2):185-197.
3. Constantin Peter, Foias Ciprian Navier-Stokes Equations. Chicago Lectures in Mathematics 1988, University of Chicago Press, Chicago, IL.
4. de Lellis Camillo, Székelyhidi László On admissibility criteria for weak solutions of the Euler equations. Arch. Ration. Mech. Anal. 2010, 195(1):225-260.
5. DiPerna R.J., Lions P.-L. Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 1989, 98(3):511-547.
6. DiPerna Ronald J., Majda Andrew J. Oscillations and concentrations in weak solutions of the incompressible fluid equations. Comm. Math. Phys. 1987, 108(4):667-689.
7. Evans Lawrence C. Partial Differential Equations. Graduate Studies in Mathematics 2010, vol. 19. American Mathematical Society, Providence, RI. second edition.
8. Iftimie Dragoş, Raugel Geneviève Some results on the Navier-Stokes equations in thin 3D domains. J. Differential Equations 2001, 169(2):281-331.
9. Serrin James The initial value problem for the Navier-Stokes equations. Nonlinear Problems 1963, 69-98. Univ. of Wisconsin Press, Madison, Wis.
10. Székelyhidi László Weak solutions to the incompressible Euler equations with vortex sheet initial data. C. R. Acad. Sci. Paris, Ser. I 2011, 349(19-20):1063-1066.
11. Székelyhidi László, Wiedemann Emil Young measures generated by ideal incompressible fluid flows. Arch. Ration. Mech. Anal. 2012, 206:333-366.