Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity

S. A. Nazarov; K. Pileckas

Rendiconti del Seminario Matematico della Università di Padova (1998)

  • Volume: 99, page 1-43
  • ISSN: 0041-8994

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Nazarov, S. A., and Pileckas, K.. "Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity." Rendiconti del Seminario Matematico della Università di Padova 99 (1998): 1-43. <http://eudml.org/doc/108473>.

@article{Nazarov1998,
author = {Nazarov, S. A., Pileckas, K.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {weighted Hölder spaces; complete asymptotic decomposition},
language = {eng},
pages = {1-43},
publisher = {Seminario Matematico of the University of Padua},
title = {Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity},
url = {http://eudml.org/doc/108473},
volume = {99},
year = {1998},
}

TY - JOUR
AU - Nazarov, S. A.
AU - Pileckas, K.
TI - Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1998
PB - Seminario Matematico of the University of Padua
VL - 99
SP - 1
EP - 43
LA - eng
KW - weighted Hölder spaces; complete asymptotic decomposition
UR - http://eudml.org/doc/108473
ER -

References

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  1. [1] C.J. Amick, Steady solutions of the Navier-Stokes equations in unbounded channels and pipes, Ann. Scuola Norm. Sup. Pisa, 4 (1977), pp. 473-513. Zbl0367.76027MR510120
  2. [2] C.J. Amick - L. E. FRAENKEL, Steady solutions of the Navier-Stokes equations representing plane flow in channels of various types, Acta Math., 144 (1980), pp. 81-152. Zbl0439.76018MR558092
  3. [3] G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations, Springer Tracts in Natural Philosophy, 38, 39 (1994). Zbl0949.35005MR1284205
  4. [4] J.G. Heywood, On uniqueness questions in the theory of viscous flow, Acta. Math., 136 (1976), pp. 61-102. Zbl0347.76016MR425390
  5. [5] L.V. Kapitanskii - K. Pileckas, On spaces of solenoidal vector fields and boundary value problems for the Navier-Stokes equations in domains with noncompact boundaries, Trudy Mat. Inst. Steklov, 159 (1983), pp. 5-36. English transl.: Proc. Math. Inst. Steklov, 159, issue 2, (1984), pp. 3-34. Zbl0585.76038MR720205
  6. [6] L.V. Kapitanskii - K. Pileckas, Certain problems of vector analysis, Zapiski Nauchn. Sem. LOMI, 138 (1984), pp. 65-85. English transl.: J. Sov. Math., 32, No. 5, (1986), pp. 469-483. Zbl0582.35012MR755909
  7. [7] V.A. Kondrat'ev, Boundary value problems for elliptic equations in domains with conical or corner points, Trudy Moskov. Mat Obshch., 16 (1967) 209-292. English transl.: Trans. Moscow Math. Soc., 16 (1967). Zbl0162.16301MR226187
  8. [8] O.A. Ladyzhenskaya, TheMathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, London, Paris (1969). Zbl0184.52603MR254401
  9. [9] O.A. Ladyzhenskaya - V.A. Solonnnikov, On some problems of vector analysis and generalized formulations of boundary value problems for the Navier-Stokes equations, Zapiski Nauchn. Sem. LOMI, 59 (1976) pp. 81-116. English transl.: J. Sov. Math., 10, No. 2 (1978), pp. 257-285. Zbl0388.35061MR467031
  10. [10] O.A. Ladyzhenskaya - V.A. Solonnnikov, On the solvability of boundary value problems for the Navier-Stokes equations in regions with noncompact boundaries, Vestnik Leningrad. Univ. (Ser. Mat. Mekh. Astr. vyp. 3), 13 (1977), pp. 39-47. English transl.: Vestnik Leningrad Univ. Math., 10 (1982), pp. 271-280. Zbl0494.35078
  11. [11] O.A. Ladyzhenskaya - V.A. Solonnnikov, Determination of the solutions of boundary value problems for stationary Stokes and Navier-Stokes equations having an unbounded Dirichlet integral, Zapiski Nauchn. Sem. LOMI, 96 (1980), pp. 117-160. English transl.: J. Sov. Math., 21, No.5 (1983), pp. 728-761. Zbl0509.35066MR579479
  12. [12] V.G. Maz'ya - B.A. Plamenevskii, Estimates in Lp and Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, Math. Nachr., 81 (1978), pp. 25-82. English transl.: Amer. Math. Soc. Transl., 123 (2) (1984), pp. 1-56. Zbl0554.35035MR492821
  13. [13] V.G. Maz'ya - B.A. Plamenevskii, On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points, Math. Nachr., 76 (1977), pp. 29-60. English transl.: Amer. Math. Soc. transl., 123 (2) (1984), pp. 57-88. Zbl0554.35036MR601608
  14. [14] V.G. Maz'ya - B.A. Plamenevskii, On the asymptotic behaviour of the solutions of differential equations in Hilbert space, Izv. Akad. Nauk SSSR. Ser. Mat., 36, No. 5 (1972), pp. 1080-1133. English transl.: Math. USSR Izvestija, 6 (1972), pp. 1067-1116. Zbl0266.34067MR352728
  15. [15] V.G. Maz'ya - B.A. Plamenevskii, On the asymptotics of the solution of the Dirichlet problem near an isolated singularity of the boundary, Vestnik Leningrad. Univ., Ser. Mat. Mekh. Astr., vyp. 3, No. 13 (1977), pp. 60-66. English transl.: Vestnik Leningrad. Univ. Math., 10 (1982). Zbl0371.35012
  16. [16] V.G. Maz'ya - S.A. Nazarov - B.A. Plamenevskii, Asymptotische Theorie ellitischer Randwertaufgaben in singulär gestörten Gebieten, Bd. II, Akademie-Verlag, (1991). 
  17. [17] S.A. Nazarov, The structure of the solutions of elliptic boundary value problems in thin domains, Vestnik Leningrad, Univ., Ser. Mat. Mekh. Astr., vyp. 2, No. 7 (1982), pp. 65-68. English transl.: Vestnik Leningrad. Univ. Math., 15 (1983). Zbl0509.35008MR664066
  18. [18] S.N. Leora - S.A. Nazarov - A.V. Proskura, Computer derivation of the limit equations for elliptic problems in thin domains, Zh. Vychisl. Mat. i Mat. Fiz., 26 (1986), pp. 1032-1048. English transl.: USSR Comput. Math. Math. Phys., 26 (1986). Zbl0626.65129MR851753
  19. [19] S.A. Nazarov, Asymptotic solution of the Navier-Stokes problem on the flow of a thin layer of fluid, Sibirsk. Mat. Zh., 31, No. 2 (1990), pp. 131-144. English transl.: Siberian Math. J., 31 (1990), pp. 296-307. Zbl0712.76037MR1065588
  20. [20] S.A. Nazarov - K. Pileckas, The Reynolds flow of a fluid in a thin threedimesional channel, Litovskii Mat. Sb., 30 (1990), pp. 772-783. English transl.: Lithuanian Math. J., 30 (1990). Zbl0715.76011MR1091657
  21. [21] S.A. Nazarov - B.A. Plamenevskii, Elliptic Boundary Value Problems in Domains with Picewise Smooth Boundary, Walter de Gruyter and Co., Berlin, (1994). 
  22. [22] K. Pileckas, Existence of solutions for the Navier-Stokes equations having an infinite dissipation of energy, in a class of domains with noncompact boundaries, Zapiski Nauchn. Sem. LOMI, 110 (1981) 180-202. English transl.: J. Sov. Math., 25, No. 1 (1984), pp. 932-947. Zbl0531.76038MR643984
  23. [23] K. Pileckas, Weighted Lq-solvability for the steady Stokes system in domains with noncompact boundaries, Math. Mod. Methods Appl. Sci. (to appear). Zbl0859.35092MR1373339
  24. [24] K. Pileckas, Classical solvability and uniform estimates for the steady Stokes system in domains with noncompact boundaries, Math. Mod. Methods Appl. Sci. (to appear). Zbl0870.35079MR1380694
  25. [25] K. Pileckas, Strong solutions of the steady nonlinear Navier-Stokes system in domains with exits to infinity, Rend. Sem. Mat. Univ. Padova (to appear). Zbl0891.35117MR1476173
  26. [26] V.A. Solonnikov - K. Pileckas, Certain spaces of solenoidal vectors and the solvability of the boundary value problem for the Navier-Stokes system of equations in domains with noncompact boundaries, Zapiski Nauchn. Sem.LOMI, 73 (1977), pp. 136-151; English transl.: J. Sov. Math., 34, No. 6 (1986), pp. 2101-2111. Zbl0612.35111MR513173
  27. [27] V.A. Solonnikov, On the solvability of boundary and initial-boundary value problems for the Navier-Stokes system in domains with noncompact boundaries, Pacific J. Math., 93, No. 2 (1981), pp. 443-458. Zbl0413.35062MR623575
  28. [28] V.A. Solonnikov, On solutions of stationary Navier-Stokes equations with an infinite Dirichlet integral, Zapiski Nauchn. Sem. LOMI, 115 (1982), pp. 257-263; English transl.: J. Sov. Math., 28, No. 5 (1985), pp. 792-799. Zbl0561.76045MR660087
  29. [29] V.A. Solonnikov, Stokes and Navier-Stokes equations in domains with noncompact boundaries, College de France Seminar, 4 (1983), pp. 240-349. Zbl0547.35102MR716521
  30. [30] V.A. Solonnikov, Boundary and initial-boundary value problems for the Navier-Stokes equations in domains with noncompact boundaries, Math. Topics in Fluid Mechanics, Pitman Research Notes in Mathematics Series, 274, eds. J. F. Rodriques, A. Sequeira (1991), pp. 117-162. Zbl0794.76025MR1204926
  31. [31] R. Temam, Navier-Stokes EquationsNorth-Holland Pub. Co., Amsterdam, New York, Tokyo (1977). Zbl0383.35057MR769654

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