A counterexample to the smoothness of the solution to an equation arising in fluid mechanics

Commentationes Mathematicae Universitatis Carolinae

Volumn 43, Issue 1, 2002, Pages 61-75

  Montgomery Smith, Stephen ^a   Pokorný, Milan ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Euler equations; Eulerian Lagrangian description of viscous fluids; Navier Stokes equations; Regularity of systems of PDE's

Indexed keywords

EID: 84867989527     PISSN: 00102628     EISSN: 12137243     Source Type: Journal    
DOI: None     Document Type: Article

References (9)

1. Chorin A.J Vorticity and Turbulence, Applied Mathematical Sciences 103, Springer-Verlag, New York, 1994
2. Constantin P An Eulerian-Lagrangian approach to the Navier-Stokes equations, preprint, 2000
3. DiPerna R.J., Majda A Oscillations and concentrations in weak solutions of the incom-pressible fluid equations, Comm. Math. Phys. 108 (1987), 667-212
4. Kiselev A.A., Ladyzhenskaya O.A On the existence and uniqueness of the solution of the nonstationary problem for a viscous, incompressible fluid (in Russian), Izv. Akad. Nauk SSSR. Ser. Mat. 21 (1957), 655-680
5. Ladyzhenskaja O.A., Solonnikov V.A., Uralceva N.N Linear and quasilinear equations of parabolic type (in Russian), Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, R.I., 1967
6. Leray J Sur le mouvement d'un liquide visqueux emplisant l'espace, Acta Math. 63 (1934), 193-248
7. Lions P.-L Mathematical Topics in Fluid Mechanics, Vol. 1, Clarendon Press, Oxford, 1996
8. Maunder C.R.F Algebraic Topology, Cambridge University Press, Cambridge-New York, 1980
9. Oru F Rôle des oscillation dans quelques problèmes d'analyse non-linéaire, Ph.D. Thesis, ENS Cachan, 1998