Navier-Stokes equations with first order boundary conditions

Journal of Mathematical Fluid Mechanics

Volumn 8, Issue 4, 2006, Pages 456-481

  Steiger, Olivier ^a  

^a UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

Navier Stokes equations; Stress free and slip boundary conditions

Indexed keywords

BOUNDARY CONDITIONS; EXTRAPOLATION; INTERPOLATION; NAVIER STOKES EQUATIONS;

DIRICHLET; SLIP BOUNDARY CONDITIONS;

FLUID DYNAMICS;

BOUNDARY CONDITIONS; EXTRAPOLATION; FLUID DYNAMICS; INTERPOLATION; NAVIER STOKES EQUATIONS;

BOUNDARY CONDITION; NAVIER-STOKES EQUATIONS;

EID: 33845783825     PISSN: 14226928     EISSN: 14226952     Source Type: Journal    
DOI: 10.1007/s00021-005-0184-4     Document Type: Article

References (23)

1. H. AMANN, Linear and quasilinear parabolic problems, Vol. I: Abstract linear theory, Birkhäuser, Basel, Boston, Berlin, 1995.
2. H. AMANN, Compact embeddings of vector-valued Sobolev and Besov spaces, Glasnik Matematicki 35 (55) (2000).
3. H. AMANN, On the strong solvability of the Navier-Stokes equations, J. Math. Fluid Mech. 2 (2000), 16-98.
4. H. AMANN, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45 (1983), 225-254.
5. H. AMANN, Dynamic theory of quasilinear parabolic equations -11, Reaction-diffusion systems, Diff. Int. Equ. 3 (1990), 13-75.
6. H. AMANN, Nonhomogeneous Navier-Stokes equations in spaces of low regularity, Topics in Mathematical Fluid Mechanics, Quaderni di Matematica 10 (2002), 13-31.
7. H. AMANN, Linear parabolic problems involving measures, RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 95 (2001), 85-119.
8. H. AMANN, Nonhomogeneous Navier-Stokes equations with integrable low-regularity data, in: Nonlinear problems in mathematical physics and related topics, II. Int. Math. Ser., 1-28, Kluwer/Plenum, New York, 2002.
9. E. B. FABES, J. E. LEWIS and N. M. RIVIÈRE, Boundary value problems for the Navier-Stokes equations, Amer. J. Math. 99 (1977), 628-668.
10. Y. GIGA, The nonstationary Navier-Stokes System with some first order boundary condition, Proc. Japan Acad. Ser. A 58 (1982), 101-104.
11. P. GRISVARD, Équations différentielles abstraites, Ann. Se. Éc. Norm. Sup. Sér. 4 (1969).
12. G. GRUBS, Functional calculus of pseudo-differential boundary problems, Progress in Math. Vol. 65, Birkhäuser, Boston, 1986.
13. p spaces, Comm. P. D. E. 15 (1990), 289-340.
14. p Sobolev spaces, Diff. Int. Equ. 8 (1995), 1013-1046.
15. G. GRUBB and V. A. SOLONNIKOV, Reduction of fundamental initial-boundary value problems for the Stokes equation to parabolic initial-boundary value problems for systems of pseudo-differential equations, J. Soviet Math. 49 (1990), 1140-1147.
16. G. GRUBB and V. A. SOLONNIKOV, Reduction of basic initial-boundary value problems for the Navier-Stokes equations to nonlinear parabolic systems of pseudodifferential equations, Zap. Nauchn. Sem. L.O.M.I. 171 (1989), 36-52.
17. G. GRUBB and V. A. SOLONNIKOV, Boundary value problems for the Navier-Stokes equations treated by pseudo-differential methods, Math. Scand. 69 (1991), 217-290.
18. p-related spaces, Ph.D. thesis, Københavens Universitet, 1993.
19. F. K. G. ODQVIST, Über die Randwertaufgabeen der Hydrodynamik zäher Flüssigkeiten, Math. Z. 32 (1930), 329-376.
20. p with boundary conditions, Stud. Math. 44 (1972), 47-60.
21. Y. SHIBITA and S. SHIMIZU, On a resolvent estimate for the Stokes System with Neumann boundary condition, Diff. Int. Equ. 16 (4) (2003), 385-426.
22. O. STEIGER, On Navier-Stokes equations with first order boundary conditions, Ph.D. thesis, Universität Zürich, 2004.
23. H. TRIEBEL, Interpolation theory, function spaces, differential operators, second ed., Johann Ambrosius Barth, Heidelberg, Leipzig, 1995.