Nonhomogeneous boundary value problem for Navier–Stokes equations in 2D symmetric unbounded domains

References

• Chipot M, Kaukalyté K, Pileckas K, et al. On nonhomogeneous boundary value problems for the stationary Navier–Stokes equations in 2D symmetric semi-infinite outlets. Analysis and Applications. 2015. https://doi.org/http://dx.doi.org/10.1142/S0219530515500268
   Web of Science ®Google Scholar
• Leray J. Étude de diverses équations intégrales non linéaire et de quelques problèmes que pose l’hydrodynamique [Nonlinear integral equations and some hydrodynamic problem]. J. Math. Pures Appl. 1933;12:1–82.
   Google Scholar
• Ladyzhenskaya OA. The mathematical theory of viscous incompressible flow. New York: Gordon and Breach; 1969.
   Google Scholar
• Ladyzhenskaya OA. Investigation of the Navier–Stokes equation for stationary motion of an incompressible fluid. Uspech Mat. Nauk. 1959;14:75–97. Russian.
   Google Scholar
• Vorovich II, Judovich VI. Stationary flows of a viscous incompressible fluid. Mat. Sbornik. 1961;53:393–428. Russian.
   Google Scholar
• Borchers W, Pileckas K. Note on the Flux Problem for Stationary Navier--Stokes equations in domains with multiply connected boundary. Acta App. Math. 1994;37:21–30.
   Web of Science ®Google Scholar
• Finn R. On the steady-state solutions of the Navier--Stokes equations III. Acta Math. 1961;105:197–244.
   Web of Science ®Google Scholar
• Fujita H. On the existence and regularity of the steady-state solutions of the Navier--Stokes theorem. J. Faculty Sci. Univ. Tokyo Sect. I. 1961;9:59–102.
   Google Scholar
• Galdi GP. On the existence of steady motions of a viscous flow with non-homogeneous conditions. Le Matematiche. 1991;66:503–524.
   Google Scholar
• Kozono H, Yanagisawa T. Leray’s problem on the stationary Navier--Stokes equations with inhomogeneous boundary data. Math. Z. 2009;262:27–39.
   Web of Science ®Google Scholar
• Amick ChJ. Existence of solutions to the nonhomogeneous steady Navier--Stokes equations. Indiana Univ. Math. J. 1984;33:817–830.
   Web of Science ®Google Scholar
• Fujita H. On stationary solutions to Navier--Stokes equation in symmetric plane domain under general outflow condition. Pitman research notes in mathematics. Vol. 388, Proceedings of international conference on Navier-Stokes equations. Theory and numerical methods, June 1997. Varenna, Italy: 1997. pp. 16–30.
   Google Scholar
• Fujita H, Morimoto H. A remark on the existence of the Navier--Stokes flow with non-vanishing outflow condition. GAKUTO Int. Ser. Math. Sci. Appl. 1997;10:53–61.
   Google Scholar
• Morimoto H. A Remark on the existence of 2-D steady Navier--Stokes flow in bounded symmetric domain under general outflow condition. J. Math. Fluid Mech. 2007;9:411–418.
   Web of Science ®Google Scholar
• Pukhnachev VV. Viscous flows in domains with a multiply connected boundary. Fursikov AV, Galdi GP, Pukhnachev VV, editors. New directions in mathematical fluid mechanics. The Alexander V. Kazhikhov memorial volume. Birkhauser: Basel; 2009. pp. 333–348.
   Google Scholar
• Pukhnachev VV. The Leray problem and the Yudovich hypothesis. Izv. Vuzov. Sev.-Kavk. Region. Nat. Sci. 2009;185–194. The special issue “Actual problems of mathematical hydrodynamics”, Russian.
   Google Scholar
• Sazonov LI. On the existence of a stationary symmetric solution of the two-dimensional fluid flow problem. Mat. Zametki. 1993;54:138–141; English Transl.: Math. Notes. 1993;54:1280--1283.
   Google Scholar
• Korobkov MV, Pileckas K, Russo R. Steady Navier--Stokes system with nonhomogeneous boundary conditions in the axially symmetric case. C. R. Mecanique. 2012;340:115–119.
   Web of Science ®Google Scholar
• Korobkov MV, Pileckas K, Russo R. On the flux problem in the theory of steady Navier--Stokes equations with nonhomogeneous boundary conditions. Arch. Rational Mech. Anal. 2013;207:185–213.
   Web of Science ®Google Scholar
• Korobkov MV, Pileckas K, Russo R. Solution of Leray’s problem for stationary Navier--Stokes equations in plane and axially symmetric spatial domains. Ann. Math. 2015;181:769–807.
   Web of Science ®Google Scholar
• Korobkov MV, Pileckas K, Russo R. The existence theorem for steady Navier--Stokes equations in the axially symmetric case. Annali della Scuola Normale Superiore di Pisa Classe di Scienze. 2015;14:233–262.
   Web of Science ®Google Scholar
• Kaulakyt\.{e} K. On nonhomogeneous boundary value problem for the steady Navier--Stokes system in domain with paraboloidal and layer type outlets to infinity. Topological Methods Nonlinear Anal. 2015;46:835–865.
   Web of Science ®Google Scholar
• Kaulakyt\.{e} K, Pileckas K. On the nonhomogeneous boundary value problem for the Navier--Stokes system in a class of unbounded domains. J. Math. Fluid Mech. 2012;14:693–716.
   Web of Science ®Google Scholar
• Neustupa J. On the steady Navier--Stokes boundary value problem in an unbounded 2D domain with arbitrary fluxes through the components of the boundary. Ann. Univ. Ferrara. 2009;55:353–365.
   Google Scholar
• Neustupa J. A new approach to the existence of weak solutions of the steady Navier--Stokes system with inhomoheneous boundary data in domains with noncompact boundaries. Arch. Rational Mech. Anal. 2010;198:331–348.
   Web of Science ®Google Scholar
• Morimoto H, Fujita H. A remark on the existence of steady Navier--Stokes flows in 2D semi-Infinite channel Infolving the general outflow condition. Mathematica Bohemica. 2001;126:457–468.
   Google Scholar
• Morimoto H, Fujita H. A remark on the existence of steady Navier--Stokes flows in a certain two-dimensional infinite channel. Tokyo J. Math. 2002;25:307–321.
   Google Scholar
• Morimoto H, Fujita H. Stationary Navier--Stokes flow in 2-Dimensional Y-shape channel under general outflow condition. In: Proceedings of the International Conference on the Navier-Stokes Equations: Theory and Numerical Methods, June 2000, Vol. 223; Varenna, Italy; 2002. p. 65–72.
   Google Scholar
• Morimoto H. Stationary Navier--Stokes flow in 2-D channels involving the general outflow condition. Vol. 4, Handbook of differential equations: stationary partial differential equations. Chapter 5, Amsterdam: Elsevier; 2007. pp. 299–353.
   Google Scholar
• Ladyzhenskaya OA, Solonnikov VA. Determination of the solutions of boundary value problems for stationary Stokes and Navier--Stokes equations having an unbounded Dirichlet integral. Zapiski Nauchn. Sem. LOMI. 1980;96:117–160; English Transl.: J. Sov. Math. 1983;21:728--761.
   Google Scholar
• Solonnikov VA. Stokes and Navier--Stokes equations in domains with noncompact boundaries, Nonlinear partial differential equations and their applications. Pitmann notes in mathematics. Vol. 3, College de France Seminar. Marshfield (WI): Pitman Publishing; 1983, pp. 240–349.
   Google Scholar
• Stein EM. Singular integrals and differentiability properties of functions. New Jersey (NJ): Princeton University Press; 1970.
   Google Scholar
• Takeshita A. A remark on Leray’s inequality. Pacific J. Math. 1993;157:151–158.
   Web of Science ®Google Scholar
• Solonnikov VA, Pileckas K. 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. 1977;73:136–151; English Transl.: J. Sov. Math. 1986;34:2101--2111.
   Google Scholar