Regularity of axially symmetric flows in a half-space in three dimensions

SIAM Journal on Mathematical Analysis

Volumn 35, Issue 6, 2004, Pages 1636-1643

  Kang, Kyungkeun ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Axially symmetric flow; Navier Stokes equations; No swirl

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; THEOREM PROVING; VECTORS;

AXIALLY SYMMETRIC FLOWS; AZIMUTHAL COMPONENTS; SPATIAL VARIABLES;

FLOW OF FLUIDS;

EID: 9744237209     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141002414421     Document Type: Article

References (18)

1. L. CAFFARELLI, R. KOHN, AND L. NIRENBERG, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math., 35 (1982), pp. 771-831.
2. P. CONSTANTIN AND C. FOIAS, Navier-Stokes Equations, Chicago Lectures in Math., University of Chicago Press, Chicago, IL, 1988.
3. p estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains, J. Funct. Anal., 102 (1991), pp. 72-94.
4. O. A. LADYZENSKAJA, Unique global solvability of the three-dimensional Cauchy problem for the Navier-Stokes equations in the presence of axial symmetry, Zap. Naucn. Sem. LOMI, 7 (1968), pp. 155-177 (in Russian).
5. O. A. LADYZENSKAJA AND G. A. SEREGIN, On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations, J. Math. Fluid Mech., 1 (1999), pp. 356-387.
6. O. A. LADYZHENSKAYA, V. A. SOLONNIKOV, AND N. N. URALCEVA, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr., 23, AMS, Providence, RI, 1968.
7. L. D. LANDAU AND E. M. LIFSHITZ, Fluid Mechanics, Addison-Wesley, Reading, MA, 1959.
8. 3, Z. Anal. Anwendungen, 18 (1999), pp. 639-649.
9. J. LERAY, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math., 63 (1934), pp. 193-248.
10. G. M. LIEBERMAN, Second Order Parabolic Differential Equations, World Scientific, River Edge, NJ, 1996.
11. F.-H. LIN, A new proof of the Caffarelli-Kohn-Nirenberg theorem, Comm. Pure Appl. Math., 51 (1998), pp. 241-257.
12. J. NEUSTUPA AND M. POKORNÝ, An interior regularity criterion for an axially symmetric suitable weak solution to the Navier-Stokes equations, J. Math. Fluid Mech., 2 (2000), pp. 381-399.
13. V. SCHEFFER, Partial regularity of solutions to the Navier-Stokes equations, Pacific J. Math., 66 (1976), pp. 535-552.
14. G. A. SEREGIN, Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary, J. Math. Fluid Mech., 4 (2002), pp. 1-29.
15. J. SERRIN, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 9 (1962), pp. 187-195.
16. H. SOHR AND W. VON WAHL, On the regularity of the pressure of weak solutions of Navier-Stokes equations, Arch. Math. (Basel), 46 (1986), pp. 428-439.
17. R. TEMAM, Navier-Stokes Equations and Nonlinear Functional Analysis, 2nd ed., CBMS-NSF Reg. Conf. Ser. in Appl. Math. 66, SIAM, Philadelphia, 1995.
18. M. R. UKHOVSKII AND V. I. IUDOVICH, Axially symmetric flows of ideal and viscous fluids filling the whole space, J. Appl. Math. Mech., 32 (1968), pp. 52-61.