Role of the pressure for validity of the energy equality for solutions of the navier-stokes equation

Journal of Dynamics and Differential Equations

Volumn 18, Issue 2, 2006, Pages 461-482

  Kukavica, Igor ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Mild solutions; Navier Stokes equations; Uniqueness

Indexed keywords

EID: 33744802345     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-006-9010-9     Document Type: Article

References (11)

1. Constantin, P., W. E, and Titi, E. S. (1994). Onsager's conjecture on the energy conservation for solutions of Euler's equation. Comm. Math. Phys. 165, 207-209.
2. Caffarelli, L., Kohn, R., and Nirenberg, L. (1982). Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math. 35, 771-831.
3. Duchon, J., and Robert, R. (2000). Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations. Nonlinearity 13, 249-255.
4. p. Arch. Rational Mech. Anal. 45, 222-240.
5. Kukavica, I. (2003). On local uniqueness of solutions of the Navier-Stokes equations with bounded initial data. J. Diff. Eq. 194, 39-50.
6. Kukavica, I. (to appear). Pressure integrability conditions for uniqueness of mild solutions of the Navier-Stokes system. J. Diff. Eq. (to appear).
7. Leray, J. (1934). Sur le mouvement d'un liquide visquex emplissant l'espace. Acta Math. 63, 193-248.
8. Lions, P. L. (1996). Mathematical Topics in Fluid Mechanics, Incompressible Models, vol. 1, Oxford Lecture Series in Mathematics and its Applications. Clarendon Press, Oxford.
9. Onsager, L. (1949). Statistical hydrodynamics. Nuovo Cimento 6 (2) (Convegno Internazionale di Meccanica Statistica), 279-287.
10. Sell, G. R. (1996). Global attractors for the three-dimensional Navier-Stokes equations. J. Dyn. Diff. Eq. 8, 1-33.
11. Serrin, J. (1963). The initial value problem for the Navier-Stokes equations. Nonlinear Problems Proceedings Symposium Madison, Wis., University of Wisconsin Press, Madison, Wis. 69-98.