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Local pressure methods in Orlicz spaces for the motion of rigid bodies in a non-Newtonian fluid with general growth conditions
Long time existence of regular solutions to non-homogeneous Navier-Stokes equations
1. | Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warsaw, Poland |
References:
[1] |
S. N. Antontzev, A. V. Kazhikhov and V. N. Monakhov, "Boundary Problems for Mechanics of Nonhomogeneous Fluids," (in Russian), Nauka, Novosibirsk, 1983. |
[2] |
O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, "Integral Representation of Functions, and Embedding Theorems," (in Russian), Izdat. "Nauka," Moscow, 1975. |
[3] |
M. Burnat and W. M. Zajączkowski, On local motion of a compressible barotropic viscous fluid with the boundary slip condition, Top. Meth. Nonlin. Anal., 10 (1997), 195-223. |
[4] |
R. Danchin and P. B. Mucha, A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space, J. Funct. Anal., 256 (2009), 881-927.
doi: 10.1016/j.jfa.2008.11.019. |
[5] |
P.-L. Lions, "Mathematical Topics in Fluid Mechanics. Vol. 1. Incompressible Models," Oxford Lecture Series in Mathematics and its Applications, 3, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1996. |
[6] |
B. Nowakowski and W. M. Zajączkowski, Global existence of solutions to Navier-Stokes equations in cylindrical domains, Appl. Math., 36 (2009), 169-182.
doi: 10.4064/am36-2-5. |
[7] |
B. Nowakowski and W. M. Zajączkowski, Global attractor for Navier-Stokes equaitons in cylindrical domains, Appl. Math., 36 (2009), 183-194.
doi: 10.4064/am36-2-6. |
[8] |
J. Rencławowicz and W. M. Zajączkowski, Large time regular solutions to the Navier-Stokes equations in cylindrical domains, Top. Meth. Nonlin. Anal., 32 (2008), 69-87. |
[9] |
W. M. Zajączkowski, Global existence of axially symmetric solutions of incompressible Navier-Stokes equations with large angular component of velocity, Colloq. Math., 100 (2004), 243-263.
doi: 10.4064/cm100-2-7. |
[10] |
W. M. Zajączkowski, Long time existence of regular solutions to the Navier-Stokes equations in cylindrical domains under boundary slip conditions, Studia Math., 169 (2005), 243-285.
doi: 10.4064/sm169-3-3. |
[11] |
W. M. Zajączkowski, Nonstationary Stokes system in Sobolev-Slobodetski spaces, Math. Ann., (2013). |
[12] |
W. M. Zajączkowski, On global regular solutions to the Navier-Stokes equations in cylindrical domains, Top. Meth. Nonlin. Anal., 37 (2011), 55-65. |
[13] |
W. M. Zajączkowski, Global special regular solutions to the Navier-Stokes equations in a cylindrical domain without the axis of symmetry, Top. Meth. Nonlin. Anal., 24 (2004), 69-105. |
[14] |
W. M. Zajączkowski, Global regular solutions to the Navier-Stokes equations in a cylinder, in "Self-Similar Solutions of Nonlinear PDE," Banach Center Publ., 74, Polish Acad. Sci., Warsaw, (2006), 235-255.
doi: 10.4064/bc74-0-15. |
[15] |
, E. Zadrzyńska and W. M. Zajączkowski,, Nonstationary Stokes system in anisotropic Sobolev spaces, (2013).
|
show all references
References:
[1] |
S. N. Antontzev, A. V. Kazhikhov and V. N. Monakhov, "Boundary Problems for Mechanics of Nonhomogeneous Fluids," (in Russian), Nauka, Novosibirsk, 1983. |
[2] |
O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, "Integral Representation of Functions, and Embedding Theorems," (in Russian), Izdat. "Nauka," Moscow, 1975. |
[3] |
M. Burnat and W. M. Zajączkowski, On local motion of a compressible barotropic viscous fluid with the boundary slip condition, Top. Meth. Nonlin. Anal., 10 (1997), 195-223. |
[4] |
R. Danchin and P. B. Mucha, A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space, J. Funct. Anal., 256 (2009), 881-927.
doi: 10.1016/j.jfa.2008.11.019. |
[5] |
P.-L. Lions, "Mathematical Topics in Fluid Mechanics. Vol. 1. Incompressible Models," Oxford Lecture Series in Mathematics and its Applications, 3, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1996. |
[6] |
B. Nowakowski and W. M. Zajączkowski, Global existence of solutions to Navier-Stokes equations in cylindrical domains, Appl. Math., 36 (2009), 169-182.
doi: 10.4064/am36-2-5. |
[7] |
B. Nowakowski and W. M. Zajączkowski, Global attractor for Navier-Stokes equaitons in cylindrical domains, Appl. Math., 36 (2009), 183-194.
doi: 10.4064/am36-2-6. |
[8] |
J. Rencławowicz and W. M. Zajączkowski, Large time regular solutions to the Navier-Stokes equations in cylindrical domains, Top. Meth. Nonlin. Anal., 32 (2008), 69-87. |
[9] |
W. M. Zajączkowski, Global existence of axially symmetric solutions of incompressible Navier-Stokes equations with large angular component of velocity, Colloq. Math., 100 (2004), 243-263.
doi: 10.4064/cm100-2-7. |
[10] |
W. M. Zajączkowski, Long time existence of regular solutions to the Navier-Stokes equations in cylindrical domains under boundary slip conditions, Studia Math., 169 (2005), 243-285.
doi: 10.4064/sm169-3-3. |
[11] |
W. M. Zajączkowski, Nonstationary Stokes system in Sobolev-Slobodetski spaces, Math. Ann., (2013). |
[12] |
W. M. Zajączkowski, On global regular solutions to the Navier-Stokes equations in cylindrical domains, Top. Meth. Nonlin. Anal., 37 (2011), 55-65. |
[13] |
W. M. Zajączkowski, Global special regular solutions to the Navier-Stokes equations in a cylindrical domain without the axis of symmetry, Top. Meth. Nonlin. Anal., 24 (2004), 69-105. |
[14] |
W. M. Zajączkowski, Global regular solutions to the Navier-Stokes equations in a cylinder, in "Self-Similar Solutions of Nonlinear PDE," Banach Center Publ., 74, Polish Acad. Sci., Warsaw, (2006), 235-255.
doi: 10.4064/bc74-0-15. |
[15] |
, E. Zadrzyńska and W. M. Zajączkowski,, Nonstationary Stokes system in anisotropic Sobolev spaces, (2013).
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