On steady compressible Navier-Stokes equations in plane domains with corners

Mathematische Annalen

Volumn 304, Issue 1, 1996, Pages 121-150

  Nazarov, S A ^a   Novotny A ^b   Pileckas, K ^c  

^a State Maritime Academy   (Russian Federation)

^b UNIVERSITÉ DE TOULON   (France)

^c UNIVERSITY OF PADERBORN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030553640     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01446288     Document Type: Article

References (54)

1. P-theory for the n-dimensional, stationary comparissible Navier-Stokes equations and the incompressible limit for compressible fluids. The equilibrium solutions. Comm. Math. Phys. 109 (1987), 229-248
2. [BV 2] Beirão da Veiga H.: Boundary value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow, Rend. Sem. Mat. Univ. Padova 79 (1988), 247-273
3. [BoPi] Borchers W., Pileckas K.: Existence, uniqueness and asymptotics of steady jets, Arch. Rat. Mech. Anal. 120 (1992), 1-49
4. [D 1] Dauge M.: Opérateur de Stokes dans des espaces de Sobolev à points sur des domains anguleux, Can. J. Math. 34(4) (1982), 853-882
5. [D 2] Dauge M.: Stationary Stokes and Navier-Stokes systems on two and three-dimensional domains with corners. Part I.: Linearized Equations, SIAM J. Math. Anal. 20(1) (1989), 74-97
6. [D 3] Dauge M.: Elliptic boundary value problems on corner domains, smoothness and asymptotics of solutions, Lecture Notes Math. 1341 (1988)
7. [Gr 1] Grisvard P.: Singularités des solutions du problème de Stokes dans un polygon, Université de Nice (preprint) (1979)
8. [Gr 2] Grisvard P.: Elliptic problems in nonsmooth domains. Boston, London, Melbourne, Pitman Pub. Co. (1985)
9. [F] Farwig R.: Stationary solutions of the Navier-Stokes equations with slip boundary conditions, Comm. Part. Diff. Eq. 14(11) (1989), 1579-1606
10. [KeOs] Kellog R.B., Osborn J.E.: A regularity result for the Stokes problem in a convex polygon, J. Funct. Anal. 21 (1976), 397-431
11. [K 1] Kondrat'ev V.: Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obsc. 16 (1967), 209-292 (in Russian); English translation in Trans. Moscow Math. Soc. 16 (1967), 227-313
12. [K 1] Kondrat'ev V.: Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obsc. 16 (1967), 209-292 (in Russian); English translation in Trans. Moscow Math. Soc. 16 (1967), 227-313
13. [K 2] Kondrat'ev V.: Asymptotic of solution of the Navier-Stokes equations near the angular point of the boundary, J. Appl. Math. Mech. 31 (1967), 125-129
14. [KoMa] Kozlov V.A., Maz'ya V.G.: On quasihomogeneous solutions to the Dirichlet problem for the Stokes system in a dihedral angle, Univ. Linköping LiTH-MAT-R-91-15 (preprint), 1991
15. [KoMaSch 1] Kozlov V.A., Maz'ya V.G., Schwab C.: On singularities of solutions to the Dirichlet problem of hydrodynamics near the vertex of a 3-D cone, Univ. Linköping LiTH-MAT-R-90-23 (preprint) (1990)
16. [KoMaSch 2] Kozlov V.A., Maz'ya V.G., Schwab C.: On singularities of solutions to the boundary value problems near the vertex of a rotational cone, Univ. Linköping LiTH-MAT-R-91-24 (preprint) (1991)
17. [MNi] Matsumura A., Nishida T.: Exterior stationary problems for the equations of motion of compressible viscous and heat conductive fluids. Proc. EQUADIFF 89. Ed. Dafermos, Ladas, Papanicolau, M. Dekker Inc. (1989), 473-479
18. [MaPl 1] Maz'ya V.G., Plamenevskii B.A.: About asymptotics of solutions of Navier-Stokes equations near edges, Dokl. Acad. Nauk SSSR 210(4) (1973), 803-806
19. [MaPl 2] Maz'ya V.G., Plamenevskii B.A.: Problem of the motion of the fluid with a free surface in a vessel with edges, Problemy Mat. Analiza 7, LGU (1979), 100-145 (in Russian)
20. [MaPl 3] Maz'ya V.G., Plamenevskii B.A.: On properties of solutions of three-dimensional problems in the elasticity and hydrodynamics in domains with isolated singular points, Din. Sploschnoj Sredy 50, Novosibirsk (1981), 99-121 (in Russian); English translation in Amer. Math. Soc. Transl. 123 (1984), 109-123
21. [MaPl 3] Maz'ya V.G., Plamenevskii B.A.: On properties of solutions of three-dimensional problems in the elasticity and hydrodynamics in domains with isolated singular points, Din. Sploschnoj Sredy 50, Novosibirsk (1981), 99-121 (in Russian); English translation in Amer. Math. Soc. Transl. 123 (1984), 109-123
22. [MaPl 4] Maz'ya V.G., Plamenevskii B.A.: First boundary value problem for the equations of hydrodynamics, Zap. Nauchn. Sem. LOMI 96 (1980), 179-196 (in Russian); English translation in J. Sov. Math. 21(5) (1983), 777-783
23. [MaPl 4] Maz'ya V.G., Plamenevskii B.A.: First boundary value problem for the equations of hydrodynamics, Zap. Nauchn. Sem. LOMI 96 (1980), 179-196 (in Russian); English translation in J. Sov. Math. 21(5) (1983), 777-783
24. [MaPl 5] Maz'ya V.G., Plamenevskii B.A.: On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points, Math. Nachr. 76 (1977), 29-60 (in Russian); English translation in Amer. Math. Soc. Transl. 123(2) (1984), 57-88
25. [MaPl 5] Maz'ya V.G., Plamenevskii B.A.: On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points, Math. Nachr. 76 (1977), 29-60 (in Russian); English translation in Amer. Math. Soc. Transl. 123(2) (1984), 57-88
26. [MaPl 6] Maz'ya V.O., Plamenevskii B.A.: Estimates in LP and Holder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems. Math. Nachr. 81 (1978), 25-82 (in Russian); English translation in Amer. Math. Soc. Transl. 123(2) (1984), 1-56
27. [MaPl 6] Maz'ya V.O., Plamenevskii B.A.: Estimates in LP and Holder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems. Math. Nachr. 81 (1978), 25-82 (in Russian); English translation in Amer. Math. Soc. Transl. 123(2) (1984), 1-56
28. [MaPlSt] Maz'ya V.G., Plamenevskii B.A., Stupelis L.I.: The three-dimensional problem about the motion of fluid with the free boundary, Differential equations and their application, Vilnius, 23 (1979), 29-153 (in Russian); English translation in Amer. Math. Soc. Transl. 123(2) (1984), 171-268
29. [MaPlSt] Maz'ya V.G., Plamenevskii B.A., Stupelis L.I.: The three-dimensional problem about the motion of fluid with the free boundary, Differential equations and their application, Vilnius, 23 (1979), 29-153 (in Russian); English translation in Amer. Math. Soc. Transl. 123(2) (1984), 171-268
30. Mizohata S.: The theory of partial differential equations, Cambridge Univ. Press (1973)
31. [NaPl] Nazarov S.A., Plamenevskii B.A.: Elliptic boundary value problems in domains with picewise smooth boundary, Valter de Gruyter and Co, Berlin (1993)
32. [No 1] Novotný A.: Steady flows of viscous compressible fluids in exterior domains under small perturbations of great potential forces, Math. Meth. Model. Appl. Sci. 3(6) (1993), 725-757
33. 2 approach, Proc. of EQUAM 92, Salvi R., Straskraba I., Eds. Math. Meth. Model. Appl. Sci. (in press)
34. p approach in domains with sufficiently smooth boundary Comm. Math. Univ. Carolinae (in press)
35. p-approach to steady flows of viscous compressible fluids in exterior domains, Arch. Rat. Mech. Anal. 126 (1994), 243-297
36. [NoPa 2] Novotný A., Padula M.: Existence and uniqueness of stationary solutions for viscous compressible heat conductive fluid with large potential and small non-potential external forces, Sib. Math. J. 34(5) (1993), 120-146
37. p-approach for steady flows of viscous compressible heat conductive gas. Math. Meth. Model. Appl. Sci. (in press)
38. [Os] Osborn V.E.: Regularity of solutions of the Stokes problem in a polygonal domain, Num. Sol. of Part. Diff. Eq. III. Synspade 1975, Academic Press (1976), 393-421
39. [Pa 1] Padula M.: A representation formula for steady solutions of a compressible fluid moving at low speed, Transp. Th. Stat. Phys. 21 (1992), 593-614
40. [Pa 2] Padula M.: Existence and uniqueness for viscous steady compressible motions, Arch. Rat. Mech. Anal. 77(2) (1987), 89-102
41. [Pa 3] Padula M.: Existence and uniqueness for viscous steady compressible motions, Proc. Sem. Fis. Mat. Trieste, Dinamica dei fluidi e dei gaz ionizzati (1982)
42. [PiZa] Pileckas K., Zajaczkowski W.: On the free boundary problem for stationary compressible Navier-Stokes equations, Comm. Math. Phys. 129 (1990), 169-204
43. [So 1] Solonnikov V.A.: Solvability of the problem of plane motion of a heavy viscous incompressible capillary liquid, partially filling a container, Izv. Akad. Nauk SSSR 43 (1977), 203-236 (in Russian); English translation in Math. USSR - Izv. 14 (1980), 193-221
44. [So 1] Solonnikov V.A.: Solvability of the problem of plane motion of a heavy viscous incompressible capillary liquid, partially filling a container, Izv. Akad. Nauk SSSR 43 (1977), 203-236 (in Russian); English translation in Math. USSR - Izv. 14 (1980), 193-221
45. [So 2] Solonnikov V.A.: On a free boundary problem for the system of Navier-Stokes equations, Trudy Sem. S.L. Sobolev 2 (1978), 127-140 (in Russian)
46. [So 3] Solonnikov V.A.: On the Stokes equation in domains with nonsmooth boundaries and on a viscous incompressible flow with a free surface, Nonlinear Part. Diff. Equations. 3, College de France Seminar (1980/1981), 340-423
47. [So 4] Solonnikov V.A.: Solvability of the three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system, Zap. Nauchn. Sem. LOMI 84 (1976), 252-285 (in Russian); English translation in J. Sov. Math. 21 (3) (1983), 427-450
48. [So 4] Solonnikov V.A.: Solvability of the three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system, Zap. Nauchn. Sem. LOMI 84 (1976), 252-285 (in Russian); English translation in J. Sov. Math. 21 (3) (1983), 427-450
49. [So 5] Solonnikov V.A.: Solvability of three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system, Partial Differential Equations. Banach Center Publ. 10 (1983), 361-403
50. [SoZa] Solonnikov V.A., Zajaczkowski W.: Neumann problem for second order elliptic equations in domains with edges on the boundary, Zap. Nauchn. Sem. LOMI 127 (1983), 7-48 (in Russian); English translation in J. Sov. Math. 27 (2) (1984), 2561-2586
51. [SoZa] Solonnikov V.A., Zajaczkowski W.: Neumann problem for second order elliptic equations in domains with edges on the boundary, Zap. Nauchn. Sem. LOMI 127 (1983), 7-48 (in Russian); English translation in J. Sov. Math. 27 (2) (1984), 2561-2586
52. [Va 1] Valli A.: On the existence of stationary solutions to compressible Navier-Stokes equations, Ann. Inst. H. Poincare, 4(1) (1987), 99-113
53. [Va 2] Valli A.: Periodic and stationary solutions for compressible Navier-Stokes equations via stability method, Ann. Sc. Norm. Sup. Pisa 4 (1983), 607-647
54. [Ze] Zeidler E.: Vorlesungen über nichtlineare functional Analysis I (Fixpunktsäte), Leipzig, (1976)