Open Access
Math. Model. Nat. Phenom.
Volume 17, 2022
Article Number 18
Number of page(s) 36
Published online 29 June 2022
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Commun. Pure Appl. Math. 12 (1959) 623–727; II, Commun. Pure Appl. Math. 17 (1964) 35-92. [CrossRef] [Google Scholar]
  3. M.E. Bogovskii, Solutions of some problems of vector analysis related to operators div and grad, Proc. Semin. S.L. Sobolev 1 (1980) 5–40 (in Russian). [Google Scholar]
  4. R. Bunoiu, A. Gaudiello and A. Leopardi, Asymptotic analysis of a Bingham fluid in a thin T-like shaped structure. J. Math Pures Appl. 123 (2019) 148–166. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Formaggia, D. Lamponi and A. Quarteroni, One dimensional models for blood flow in arteries. J. Eng. Math. 47 (2003) 251–276. [CrossRef] [Google Scholar]
  6. P. Galdi, R. Rannacher, A.M. Robertson and S. Turek, Hemodynamical Flows, Modeling, Analysis and Simulation. Oberwolfach Seminars, V.37, Birkhauser, Basel, Boston, Berlin (2008). [Google Scholar]
  7. P. Galdi, An Introduction to the Mathematical Theory of Navier-Stokes Equations. Springer (1994). [Google Scholar]
  8. L.V. Kapitanskii and K. Pileckas, Certain problems of vector analysis, Zapiski Nauchn. Sem. LOMI, 1984, 138, 65-85 Engl. transl. Sov. Math. 32 (1986) 469–483. [CrossRef] [Google Scholar]
  9. N. Kloviene and K. Pileckas, Non-stationary Poiseuille-type solutions for the second-grade fluid flow. Lithuanian Math. J. 52 (2012) 155–171. [CrossRef] [MathSciNet] [Google Scholar]
  10. N. Kloviene and K. Pileckas, The second grade fluid flow problem in an infinite pipe. Asymptotic Anal. 83 (2013) 237–262. [CrossRef] [MathSciNet] [Google Scholar]
  11. O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Fluid. Gordon and Breach (1969). [Google Scholar]
  12. O.A. Ladyzhenskaya and V.A. Solonnikov, On some problems of vector analysis and generalized formulations of boundary value problems for the Navier-Stokes equations. Zapiski Nauchn. Sem. LOMI 59 (1976) 81-116. English Transl.: J. Sov. Math. 10 (1978) 257–285. [Google Scholar]
  13. O.A. Ladyzhenskaya and N.N. Ural'ceva, Linear and Quasi-Linear Elliptic Equations. Academic Press, New York (1968). [Google Scholar]
  14. E.M. Landis, Second Order Elliptic and Parabolic Equations. Nauka, Moscow (1971). [Google Scholar]
  15. E. Marusic-Paloka, Steady flow of a non-Newtonian fluid in unbounded channels and pipes. Math. Models Methods Appl. Sci. 10 (2000) 1425–1445. [CrossRef] [MathSciNet] [Google Scholar]
  16. E. Marusic-Paloka and I. Pazanin, A note on Kirchhoff junction rule for power-law fluids. Zeitschrift für Naturforschung A 70 (2015) 695–702. [CrossRef] [Google Scholar]
  17. A. Nachit, G. Panasenko and A.M. Zine, Asymptotic partial domain decomposition in thin tube structures: numerical experiments. Int. J. Multiscale Comput. Eng. 11 (2013) 407–441. [CrossRef] [Google Scholar]
  18. S.A. Nazarov and B.A. Plamenevskiy, Elliptic Problems in Domains with Piecewise Smooth Boundary. Nauka, Moscow (1991). [Google Scholar]
  19. O.A. Oleinik and G.A. Yosifian, On the asymptotic behaviour at infinity of solutions in linear elasticity. Arch. Rat. Mech. Anal. 78 (1982) 29–53. [CrossRef] [Google Scholar]
  20. G. Panasenko, Asymptotic expansion of the solution of Navier-Stokes equation in a tube structure, C.R. Acad. Sci. Paris 326, Série IIb (1998) 867–872. [CrossRef] [MathSciNet] [Google Scholar]
  21. G. Panasenko, Multi-scale Modeling for Structures and Composites. Springer, Dordrecht (2005). [Google Scholar]
  22. G. Panasenko and K. Pileckas, Divergence equation in thin-tube structure. Applicable Anal. 94 (2015) 1450–1459. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Panasenko and K. Pileckas, Flows in a tube structure: equation on the graph. J. Math. Phys. 55 (2014) 081505. [CrossRef] [MathSciNet] [Google Scholar]
  24. G. Panasenko and K. Pileckas, Asymptotic analysis of the non-steady Navier-Stokes equations in a tube structure. I. The case without boundary layer-in-time. Nonlinear Anal. Series A, Theory Methods Appl. 122 (2015) 125–168. [CrossRef] [Google Scholar]
  25. G. Panasenko, K. Pileckas and B. Vernescu, Steady state non-Newtonian flow in thin tube structure: equation on the graph. Algebra Anal. 33 (2021) 197–214. [Google Scholar]
  26. G. Panasenko, K. Pileckas and B. Vernescu, Steady state non-Newtonian flow with strain rate dependent viscosity in domains with cylindrical outlets to infinity. Nonlinear Anal.: Modeling Controle 26 (2021) 1166–1199. [CrossRef] [Google Scholar]
  27. G. Panasenko and B. Vernescu, Non-Newtonian flows in domains with non-compact boundaries. Nonlinear Anal. A 183 (2019) 214–229. [CrossRef] [Google Scholar]
  28. K. Pileckas, Navier-Stokes system in domains with cylindrical outlets to infinity. Leray's problem, Handbook of Mathematical Fluid Dynamics, 4. Elsevier (2007), Chap. 8, p. 445–647. [CrossRef] [Google Scholar]
  29. K. Pileckas, Weighted Lq -solvability of the steady Stokes system in domains with incompact boundaries. Math. Models Methods Appl. Sci. 6 (1996) 97–136. [CrossRef] [Google Scholar]
  30. K. Pileckas, On the non-stationary linearized Navier-Stokes problem in domains with cylindrical outlets to infinity. Math. Ann. 332 (2005) 395–419. [CrossRef] [MathSciNet] [Google Scholar]
  31. K. Pileckas, A. Sequeira and J.H. Videman, Steady flows of viscoelastic fluids in domains with outlets to infinity. J. Math. Fluid Mech. 2 (2000) 185–218. [CrossRef] [MathSciNet] [Google Scholar]
  32. K. Rajagopal and A. Gupta, On a class of exact solutions to the equations of motion of a 2D grade fluids. J. Eng. Sci. 19 (1981) 1009–1014. [CrossRef] [Google Scholar]
  33. K. Rajagopal, A note on unsteady unidirectional flows of a non-Newtonian fluid. Int. J. Nonlinear Mech. 17 (1982) 369–373. [CrossRef] [Google Scholar]

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