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Global existence of strong solutions for $2$-dimensional Navier-Stokes equations on exterior domains with growing data at infinity
1. | Dipartimento di Matematica e Fisica ``Ennio De Giorgi'', Università del Salento, Via per Arnesano, Lecce 73100, Italy |
2. | Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261 |
3. | Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt |
References:
[1] |
D. Chae, Nonexistence of asymptocially self-similar singularities in the Euler and Navier-Stokes equations, Math. Ann., 338 (2007), 435-449.
doi: 10.1007/s00208-007-0082-6. |
[2] |
F. Crispo and P. Maremonti, An interpolation inequality in exterior domains, Rend. Sem. Mat. Univ. Padova, 112 (2004), 11-39. |
[3] |
D. Fang, B. Han and T. Zhang, Global wellposedness result for density-dependent incompressible viscous fluid in $\mathbb{R}^2$ with linearly growing initial velocity, Math. Meth. Appl. Sciences, 36 (2013), 921-935.
doi: 10.1002/mma.2649. |
[4] |
G. P. Galdi, An Introduction to the Navier-Stokes Initial-boundary Value Problem, Adv. Math. Fluid Mech., Birkhäuser, Basel, 2000. |
[5] |
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Steady-state Problems, 2nd edition. Springer Monographs in Mathematics, New York, 2011.
doi: 10.1007/978-0-387-09620-9. |
[6] |
J. G. Heywood, The Navier-Stokes equations: on the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), 639-681.
doi: 10.1512/iumj.1980.29.29048. |
[7] |
M. Hieber and O. Sawada, The Navier-Stokes equations in $\mathbb{R}^{N}$ with linearly growing initial data, Arch. Rational Mech. Anal., 175 (2005), 269-285.
doi: 10.1007/s00205-004-0347-0. |
[8] |
M. Hieber, A. Rhandi and O. Sawada, The Navier-Stokes flow for globally Lipschitz continuous initial data, in RIMS Kôkyûroku Bessatsu, vol. B1, Res. Inst. Math. Sci. (RIMS), Kyoto, 2007, 159-165. |
[9] |
T. Hishida, An existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle, Arch. Rational Mech. Anal., 150 (1999), 307-348.
doi: 10.1007/s002050050190. |
[10] |
O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Science Publishers, New York-London (1963). |
[11] |
J. Leray, Sur le mouvement d'un liquide visquex emplissant l'espace, Acta Math., 63 (1996), 193-248.
doi: 10.1007/BF02547354. |
[12] |
J. L. Lions, Espaces intermédiaires entre espaces Hilbertiens et applications, Bull. Math. Soc. Sci. Math. Phys. R. P. Roumaine, 2 (1958), 419-432. |
[13] |
J. Nečas, M. Růžička and V. Šverák, On self-similiar solutions of the Navier-Stokes equations, Acta Math., 176 (1996), 283-294. |
[14] |
O. Sawada, The Navier-Stokes flow with linearly growing initial velocity in the whole space, Bol. Soc. Parana. Mat., 22 (2004), 75-96.
doi: 10.5269/bspm.v22i2.7484. |
[15] |
T.-P. Tsai, On Leray's self-similiar solutions of the Navier-Stokes equations satisfying local energy estimates, Arch. Ration. Mech. Anal., 143 (1998), 29-51. Erratum 147 (1999), 363.
doi: 10.1007/s002050050099. |
show all references
References:
[1] |
D. Chae, Nonexistence of asymptocially self-similar singularities in the Euler and Navier-Stokes equations, Math. Ann., 338 (2007), 435-449.
doi: 10.1007/s00208-007-0082-6. |
[2] |
F. Crispo and P. Maremonti, An interpolation inequality in exterior domains, Rend. Sem. Mat. Univ. Padova, 112 (2004), 11-39. |
[3] |
D. Fang, B. Han and T. Zhang, Global wellposedness result for density-dependent incompressible viscous fluid in $\mathbb{R}^2$ with linearly growing initial velocity, Math. Meth. Appl. Sciences, 36 (2013), 921-935.
doi: 10.1002/mma.2649. |
[4] |
G. P. Galdi, An Introduction to the Navier-Stokes Initial-boundary Value Problem, Adv. Math. Fluid Mech., Birkhäuser, Basel, 2000. |
[5] |
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Steady-state Problems, 2nd edition. Springer Monographs in Mathematics, New York, 2011.
doi: 10.1007/978-0-387-09620-9. |
[6] |
J. G. Heywood, The Navier-Stokes equations: on the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), 639-681.
doi: 10.1512/iumj.1980.29.29048. |
[7] |
M. Hieber and O. Sawada, The Navier-Stokes equations in $\mathbb{R}^{N}$ with linearly growing initial data, Arch. Rational Mech. Anal., 175 (2005), 269-285.
doi: 10.1007/s00205-004-0347-0. |
[8] |
M. Hieber, A. Rhandi and O. Sawada, The Navier-Stokes flow for globally Lipschitz continuous initial data, in RIMS Kôkyûroku Bessatsu, vol. B1, Res. Inst. Math. Sci. (RIMS), Kyoto, 2007, 159-165. |
[9] |
T. Hishida, An existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle, Arch. Rational Mech. Anal., 150 (1999), 307-348.
doi: 10.1007/s002050050190. |
[10] |
O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Science Publishers, New York-London (1963). |
[11] |
J. Leray, Sur le mouvement d'un liquide visquex emplissant l'espace, Acta Math., 63 (1996), 193-248.
doi: 10.1007/BF02547354. |
[12] |
J. L. Lions, Espaces intermédiaires entre espaces Hilbertiens et applications, Bull. Math. Soc. Sci. Math. Phys. R. P. Roumaine, 2 (1958), 419-432. |
[13] |
J. Nečas, M. Růžička and V. Šverák, On self-similiar solutions of the Navier-Stokes equations, Acta Math., 176 (1996), 283-294. |
[14] |
O. Sawada, The Navier-Stokes flow with linearly growing initial velocity in the whole space, Bol. Soc. Parana. Mat., 22 (2004), 75-96.
doi: 10.5269/bspm.v22i2.7484. |
[15] |
T.-P. Tsai, On Leray's self-similiar solutions of the Navier-Stokes equations satisfying local energy estimates, Arch. Ration. Mech. Anal., 143 (1998), 29-51. Erratum 147 (1999), 363.
doi: 10.1007/s002050050099. |
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