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Infinite-energy solutions for the Navier-Stokes equations in a strip revisited
1. | University of Surrey, Guildford, Gu27XH, Surrey, United Kingdom |
2. | Department of Mathematics, University of Surrey, Guildford, GU2 7XH |
References:
[1] |
F. Abergel, Attractor for a Navier-Stokes flow in an unbounded domain. Attractors, inertial manifolds and their approximation (Marseille-Luminy, 1987). RAIRO Model. Math. Anal. Numer., 23 (1989), 359-370. |
[2] |
F. Abergel, Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains, J. Differential Equations, 83 (1990), 85-108.
doi: 10.1016/0022-0396(90)90070-6. |
[3] |
A. Afendikov and A. Mielke, Dynamical properties of spatially non-decaying 2D Navier-Stokes flows with Kolmogorov forcing in an infinite strip, J. Math. Fluid Mech., 7 (2005), 51-67.
doi: 10.1007/s00021-004-0131-9. |
[4] |
H. Amann, On the strong solvability of the Navier-Stokes equations, Jour. Math.Fluid Mechanics, 2 (2000), 16-98.
doi: 10.1007/s000210050018. |
[5] |
A. Babin, Asymptotic Expansions at infinity of a strongly perturbed Poiseuille flow, Advances in Soviet Math., 10 (1992), 1-83. |
[6] |
A. Babin, The attractor of a Navier-Stokes system in an unbounded channel-like domain, J. Dynam. Differential Equations, 4 (1992), 555-584.
doi: 10.1007/BF01048260. |
[7] |
A. Babin and M.Vishik, Attractors of partial differential evolution equations in an unbounded domain, Proc. Roy. Soc. Edinburgh Sect. A, 116 (1990), 221-243.
doi: 10.1017/S0308210500031498. |
[8] |
A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, Nauka, Moscow, 1989; North Holland, Amsterdam, 1992. |
[9] |
M. Efendiev and S. Zelik, The attractor for a nonlinear reaction-diffusion system in an unbounded domain, Comm. Pure Appl. Math., 54 (2001), 625-688.
doi: 10.1002/cpa.1011. |
[10] |
Y. Giga, S. Matsui and O. Sawada, Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity, J. Math. Fluid Mech., 3 (2001), 302-315.
doi: 10.1007/PL00000973. |
[11] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840. Springer-Verlag, Berlin-New York, 1981. |
[12] |
P. Lemarie-Rieusset, Recent developments in the Navier-Stokes problem, Chapman & Hall/CRC Research Notes in Mathematics, 431. Chapman & Hall/CRC, Boca Raton, FL, 2002.
doi: 10.1201/9781420035674. |
[13] |
A. Mielke and G. Schneider, Attractors for modulation equations on unbounded domains - existence and comparison, Nonlinearity, 8 (1995), 743-768. |
[14] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in Handbook of Differential Equations: Evolutionary Equations, Vol. IV, 103-200, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008.
doi: 10.1016/S1874-5717(08)00003-0. |
[15] |
J. Pennant and S. Zelik, Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in $mathbb{R}^{3}$, Comm. Pure Appl. Anal., 12 (2013), 461-480. |
[16] |
S. Revina and V. Yudovich, $L^p$-estimates for the resolvent of the Stokes operator in an infinite cylinder, (Russian) Mat. Sb., 187 (1996), 97-118; translation in Sb. Math., 187 (1996), 881-902.
doi: 10.1070/SM1996v187n06ABEH000139. |
[17] |
O. Sawada and Y. Taniuchi, A remark on $L^\infty$-solutions to the 2D Navier-Stokes equations, J. Math. Fluid Mech., 9 (2007), 533-542.
doi: 10.1007/s00021-005-0212-4. |
[18] |
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland, Amsterdam New York-Oxford, 1977. |
[19] |
R. Temam, Infnite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematics Series, Springer, New York-Berlin, 1988; 2nd ed., New York, 1997. |
[20] |
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978. |
[21] |
S. Zelik, Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip, Glasg. Math. J., 49 (2007), 525-588.
doi: 10.1017/S0017089507003849. |
[22] |
S. Zelik, Weak spatially nondecaying solutions of 3D Navier-Stokes equations in cylindrical domains, Instability in models connected with fluid flows. II, 255-327, Int. Math. Ser. (N. Y.), 7, Springer, New York, 2008.
doi: 10.1007/978-0-387-75219-8_6. |
[23] |
S. Zelik, Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity, Comm. Pure Appl. Math., 56 (2003), 584-637.
doi: 10.1002/cpa.10068. |
[24] |
S. Zelik, Infinite energy solutions for damped Navier-Stokes equations in $\mathbb{R}^2$, Jour. Math. Fluid Mech., 15 (2013), 717-745.
doi: 10.1007/s00021-013-0144-3. |
show all references
References:
[1] |
F. Abergel, Attractor for a Navier-Stokes flow in an unbounded domain. Attractors, inertial manifolds and their approximation (Marseille-Luminy, 1987). RAIRO Model. Math. Anal. Numer., 23 (1989), 359-370. |
[2] |
F. Abergel, Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains, J. Differential Equations, 83 (1990), 85-108.
doi: 10.1016/0022-0396(90)90070-6. |
[3] |
A. Afendikov and A. Mielke, Dynamical properties of spatially non-decaying 2D Navier-Stokes flows with Kolmogorov forcing in an infinite strip, J. Math. Fluid Mech., 7 (2005), 51-67.
doi: 10.1007/s00021-004-0131-9. |
[4] |
H. Amann, On the strong solvability of the Navier-Stokes equations, Jour. Math.Fluid Mechanics, 2 (2000), 16-98.
doi: 10.1007/s000210050018. |
[5] |
A. Babin, Asymptotic Expansions at infinity of a strongly perturbed Poiseuille flow, Advances in Soviet Math., 10 (1992), 1-83. |
[6] |
A. Babin, The attractor of a Navier-Stokes system in an unbounded channel-like domain, J. Dynam. Differential Equations, 4 (1992), 555-584.
doi: 10.1007/BF01048260. |
[7] |
A. Babin and M.Vishik, Attractors of partial differential evolution equations in an unbounded domain, Proc. Roy. Soc. Edinburgh Sect. A, 116 (1990), 221-243.
doi: 10.1017/S0308210500031498. |
[8] |
A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, Nauka, Moscow, 1989; North Holland, Amsterdam, 1992. |
[9] |
M. Efendiev and S. Zelik, The attractor for a nonlinear reaction-diffusion system in an unbounded domain, Comm. Pure Appl. Math., 54 (2001), 625-688.
doi: 10.1002/cpa.1011. |
[10] |
Y. Giga, S. Matsui and O. Sawada, Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity, J. Math. Fluid Mech., 3 (2001), 302-315.
doi: 10.1007/PL00000973. |
[11] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840. Springer-Verlag, Berlin-New York, 1981. |
[12] |
P. Lemarie-Rieusset, Recent developments in the Navier-Stokes problem, Chapman & Hall/CRC Research Notes in Mathematics, 431. Chapman & Hall/CRC, Boca Raton, FL, 2002.
doi: 10.1201/9781420035674. |
[13] |
A. Mielke and G. Schneider, Attractors for modulation equations on unbounded domains - existence and comparison, Nonlinearity, 8 (1995), 743-768. |
[14] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in Handbook of Differential Equations: Evolutionary Equations, Vol. IV, 103-200, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008.
doi: 10.1016/S1874-5717(08)00003-0. |
[15] |
J. Pennant and S. Zelik, Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in $mathbb{R}^{3}$, Comm. Pure Appl. Anal., 12 (2013), 461-480. |
[16] |
S. Revina and V. Yudovich, $L^p$-estimates for the resolvent of the Stokes operator in an infinite cylinder, (Russian) Mat. Sb., 187 (1996), 97-118; translation in Sb. Math., 187 (1996), 881-902.
doi: 10.1070/SM1996v187n06ABEH000139. |
[17] |
O. Sawada and Y. Taniuchi, A remark on $L^\infty$-solutions to the 2D Navier-Stokes equations, J. Math. Fluid Mech., 9 (2007), 533-542.
doi: 10.1007/s00021-005-0212-4. |
[18] |
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland, Amsterdam New York-Oxford, 1977. |
[19] |
R. Temam, Infnite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematics Series, Springer, New York-Berlin, 1988; 2nd ed., New York, 1997. |
[20] |
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978. |
[21] |
S. Zelik, Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip, Glasg. Math. J., 49 (2007), 525-588.
doi: 10.1017/S0017089507003849. |
[22] |
S. Zelik, Weak spatially nondecaying solutions of 3D Navier-Stokes equations in cylindrical domains, Instability in models connected with fluid flows. II, 255-327, Int. Math. Ser. (N. Y.), 7, Springer, New York, 2008.
doi: 10.1007/978-0-387-75219-8_6. |
[23] |
S. Zelik, Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity, Comm. Pure Appl. Math., 56 (2003), 584-637.
doi: 10.1002/cpa.10068. |
[24] |
S. Zelik, Infinite energy solutions for damped Navier-Stokes equations in $\mathbb{R}^2$, Jour. Math. Fluid Mech., 15 (2013), 717-745.
doi: 10.1007/s00021-013-0144-3. |
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