×

zbMATH — the first resource for mathematics

A uniqueness theorem for nonstationary Navier-Stokes flow past an obstacle. (English) Zbl 0437.76032

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] K.I. Babenko , On stationary solutions of the problem of flow past a body of a viscous incompressible fluid , Math. USSR-Sb. , 20 , no. 1 ( 1973 ), pp. 1 - 25 . Zbl 0285.76009 · Zbl 0285.76009 · doi:10.1070/SM1973v020n01ABEH001823 · eudml:70519
[2] J.R. Cannon - G.H. Knightly , Some continuous dependence theorens for viscous fluid motions, SIA M J. Appl. Math. , 18 ( 1970 ), pp. 627 - 640 . MR 269967 | Zbl 0202.37202 · Zbl 0202.37202 · doi:10.1137/0118055
[3] J.R. Cannon - G.H. Knightly , A note on the Cauchy problem for the Navier-Stokes equations , SIAM J. Appl. Math. , 18 ( 1970 ), pp. 641 - 644 . MR 270004 | Zbl 0202.37203 · Zbl 0202.37203 · doi:10.1137/0118056
[4] R. Finn , An energy theorem for viscous fluid motions , Arch. Rational Mech. Anal. , 6 ( 1960 ), pp. 371 - 381 . MR 166497 | Zbl 0096.41303 · Zbl 0096.41303 · doi:10.1007/BF00276169
[5] R. Finn , On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems , Arch. Rational Mech. Anal. , 19 ( 1965 ), pp. 363 - 406 . MR 182816 | Zbl 0149.44606 · Zbl 0149.44606 · doi:10.1007/BF00253485
[6] A. Friedman , Partial Differential Equations , Holt, Rinehart and Winston , New York , 1969 . MR 445088 | Zbl 0224.35002 · Zbl 0224.35002
[7] D. Graffi , Sul teorema di unicità nella dinamica dei fluidi , Ann. Mat. Pura Appl. , 50 ( 1960 ), pp. 379 - 388 . MR 122198 | Zbl 0102.41103 · Zbl 0102.41103 · doi:10.1007/BF02414524
[8] J.G. Heywood , The exterior nonstationary problem for the Navier-Stokes equations , Acta Math. , 129 ( 1972 ), pp. 11 - 34 . MR 609550 | Zbl 0237.35074 · Zbl 0237.35074 · doi:10.1007/BF02392212
[9] J.G. Heywood , On nonstationary Stokes flow past an obstacle , Indiana Univ. Math. J. , 24 ( 1974 ), pp. 271 - 284 . MR 355376 | Zbl 0315.35074 · Zbl 0315.35074 · doi:10.1512/iumj.1974.24.24025
[10] J.G. Heywood , On some paradoxes concerning two-dimensional Stokes flow past an obstacle , Indiana Univ. Math. J. , 24 ( 1974 ), pp. 443 - 450 . MR 410123 | Zbl 0315.35075 · Zbl 0315.35075 · doi:10.1512/iumj.1974.24.24035
[11] J.G. Heywood , On uniqueness questions in the theory of viscous flow , Acta Math. , 136 ( 1976 ), pp. 61 - 102 . MR 425390 | Zbl 0347.76016 · Zbl 0347.76016 · doi:10.1007/BF02392043
[12] E. Hopf , Ein allgemeiner Endlichkeitssatz der Hydrodynamik , Math. Ann. , 117 ( 1940 -41), pp. 764 - 775 . MR 5003 | Zbl 0024.13505 | JFM 67.0842.02 · Zbl 0024.13505 · doi:10.1007/BF01450040 · eudml:160071
[13] G.H. Knightly , A Cauchy problem for the Navier-Stokes equations in Rn , SIAM J. Math. Anal. , 3 ( 1972 ), pp. 506 - 511 . MR 312093 | Zbl 0246.76021 · Zbl 0246.76021 · doi:10.1137/0503048
[14] G.H. Knightly , Some asymptotic properties of solutions of the Navier-Stokes equations , to appear in the Proceedings International Symposium on Dynamical Systems, Gainsville , 1976 . MR 460929 | Zbl 0547.35099 · Zbl 0547.35099
[15] O.A. Ladyzhenskaya , The Mathematical Theory of Viscous Incompressible Flow , II Ed., Gordon and Breach , New York , 1969 . MR 254401 | Zbl 0184.52603 · Zbl 0184.52603
[16] J. Leray , Etude de diverses équations integrales non linéaires et de quelques problèmes que pose l’Hydrodynamique , J. Math. Pures Appl. , 9 ( 1933 ), pp. 1 - 82 ; Les problèmes non linéaires , Enseignement Math. , 35 ( 1936 ), pp. 139 - 151 . Zbl 0006.16702 · Zbl 0006.16702 · eudml:235182
[17] C.M. Ma , On square-summability and uniqueness questions concerning nonstationary Stokes flow in an exterior domain , to appear Arch. Rational Mech. Anal. MR 525220 | Zbl 0412.76026 · Zbl 0412.76026 · doi:10.1007/BF00248723
[18] J Nečas , Les méthodes directes en théorie des équations elliptiques , Masson , Paris , 1967 . MR 227584 · Zbl 1225.35003
[19] G. Prodi , Teoremi di tipo locale per il sistema di Navier-Stokes e stabilità delle soluzioni stazionarie , Rend. Sem. Mat. Univ. Padova , 32 ( 1962 ), pp. 374 - 397 . Numdam | MR 189354 | Zbl 0108.28602 · Zbl 0108.28602 · numdam:RSMUP_1962__32__374_0 · eudml:107089
[20] S. Rionero - G.P. Galdi , On the uniqueness of viscous fluid motions , Arch. Rational Mech. Anal. , 62 ( 1976 ), pp. 295 - 301 . MR 418634 | Zbl 0351.35070 · Zbl 0351.35070 · doi:10.1007/BF00280017
[21] M. Shinbrot - S. Kaniel , The initial value problem for the Navier-Stokes equations , Arch. Rational Mech. Anal. , 21 ( 1966 ), pp. 270 - 285 . MR 192215 | Zbl 0148.45504 · Zbl 0148.45504 · doi:10.1007/BF00282248
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.