@article{RSMUP_1998__99__1_0, author = {Nazarov, S. A. and Pileckas, K.}, title = {Asymptotics of solutions to {Stokes} and {Navier-Stokes} equations in domains with paraboloidal outlets to infinity}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {1--43}, publisher = {Seminario Matematico of the University of Padua}, volume = {99}, year = {1998}, mrnumber = {1636654}, zbl = {0909.35104}, language = {en}, url = {http://www.numdam.org/item/RSMUP_1998__99__1_0/} }
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 SP - 1 EP - 43 VL - 99 PB - Seminario Matematico of the University of Padua UR - http://www.numdam.org/item/RSMUP_1998__99__1_0/ LA - en ID - RSMUP_1998__99__1_0 ER -
%0 Journal Article %A Nazarov, S. A. %A Pileckas, K. %T Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity %J Rendiconti del Seminario Matematico della Università di Padova %D 1998 %P 1-43 %V 99 %I Seminario Matematico of the University of Padua %U http://www.numdam.org/item/RSMUP_1998__99__1_0/ %G en %F RSMUP_1998__99__1_0
Nazarov, S. A.; 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, Tome 99 (1998), pp. 1-43. http://www.numdam.org/item/RSMUP_1998__99__1_0/
[1] Steady solutions of the Navier-Stokes equations in unbounded channels and pipes, Ann. Scuola Norm. Sup. Pisa, 4 (1977), pp. 473-513. | Numdam | MR | Zbl
,[2] 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. | MR | Zbl
-[3] An introduction to the mathematical theory of the Navier-Stokes equations, Springer Tracts in Natural Philosophy, 38, 39 (1994). | MR | Zbl
,[4] On uniqueness questions in the theory of viscous flow, Acta. Math., 136 (1976), pp. 61-102. | MR | Zbl
,[5] 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. | MR | Zbl
- ,[6] 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. | MR | Zbl
- ,[7] 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). | MR | Zbl
,[8] Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, London, Paris (1969). | MR | Zbl
[9] 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. | MR | Zbl
- ,[10] 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. | Zbl
- ,[11] 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. | MR | Zbl
- ,[12] 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. | MR | Zbl
- ,[13] 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. | MR | Zbl
- ,[14] 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. | MR | Zbl
- ,[15] 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). | Zbl
- ,[16] Asymptotische Theorie ellitischer Randwertaufgaben in singulär gestörten Gebieten, Bd. II, Akademie-Verlag, (1991).
- - ,[17] 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). | MR | Zbl
,[18] 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). | MR | Zbl
- - ,[19] 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. | MR | Zbl
,[20] 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). | MR | Zbl
- ,[21] Elliptic Boundary Value Problems in Domains with Picewise Smooth Boundary, Walter de Gruyter and Co., Berlin, (1994).
- ,[22] 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. | MR | Zbl
,[23] Weighted Lq-solvability for the steady Stokes system in domains with noncompact boundaries, Math. Mod. Methods Appl. Sci. (to appear). | MR | Zbl
,[24] Classical solvability and uniform estimates for the steady Stokes system in domains with noncompact boundaries, Math. Mod. Methods Appl. Sci. (to appear). | MR | Zbl
,[25] Strong solutions of the steady nonlinear Navier-Stokes system in domains with exits to infinity, Rend. Sem. Mat. Univ. Padova (to appear). | Numdam | MR | Zbl
,[26] 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. | MR | Zbl
- ,[27] 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. | MR | Zbl
,[28] 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. | MR | Zbl
,[29] Stokes and Navier-Stokes equations in domains with noncompact boundaries, College de France Seminar, 4 (1983), pp. 240-349. | MR | Zbl
,[30] 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. | MR | Zbl
,[31] Navier-Stokes Equations North-Holland Pub. Co., Amsterdam, New York, Tokyo (1977). | MR | Zbl
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