On local uniqueness of weak solutions of the Navier-Stokes system with bounded initial data

Journal of Differential Equations

Volumn 194, Issue 1, 2003, Pages 39-50

  Kukavica, Igor ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Mild solutions; Navier Stokes equations; Nonuniqueness; Weak solutions

Indexed keywords

EID: 0141726762     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00153-0     Document Type: Article

References (12)

1. P. Constantin, C. Foias, Navier Stokes Equations, Chicago Lectures in Mathematics, University of Chicago, Chicago/London, 1988.
2. C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971) 587-588.
3. p, Arch. Rational Mech. Anal. 45 (1972) 222-240.
4. C. Foias, O. Manley, R. Rosa, R. Temam, Navier-Stokes Equations and Turbulence, Encyclopedia of Mathematics and its Applications, Vol. 83, Cambridge University Press, Cambridge, 2001.
5. p, J. Funct. Anal. 152 (1998) 447-466.
6. m, with applications to weak solutions, Math. Z. 187 (1984) 471-480.
7. H. Koch, D. Tataru, Well-posedness for the Navier Stokes equations, Adv. Math. 157 (2001) 22-35.
8. C. Sadosky, Interpolation of Operators and Singular Integrals: An Introduction to Harmonic Analysis, Marcel Dekker, Inc., New York and Basel, 1979.
9. E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970.
10. E.M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993.
11. R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis, 3rd Revised Edition, North-Holland, Amsterdam, 1984.
12. F.B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math. 38 (1981) 29-40.