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On the Hamiltonian dynamics and geometry of the Rabinovich system
On a generalized Boussinesq model around a rotating obstacle: Existence of strong solutions
1. | Universidad Nacional de Colombia-Medellín, Escuela de Matemáticas, Medellìn, A.A. 3840, Colombia |
2. | Departamento de Matemáticas, Universidad Católica del Norte, Av. Angamos 0610, Casilla 1280, Antofagasta, Chile |
References:
[1] |
J. Bergh and J. Löfström, "Interpolation Spaces. An Introduction," Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. |
[2] |
J. L. Boldrini and S. Lorca, The initial value problem for a generalized Boussinesq model, Nonlinear Analysis, 36 (1999), 457-480.
doi: 10.1016/S0362-546X(97)00635-4. |
[3] |
P. Braz e Silva, M. A. Rojas-Medar and E. J. Villamizar-Roa, Strong solutions for the nonhomogeneous Navier-Stokes equations in unbounded domains, Math. Methods Appl. Sci., 33 (2010), 358-372. |
[4] |
L. C. F. Ferreira and E. J. Villamizar-Roa, Well-posedness and asymptotic behaviour for the convection problem in $\mathbb{R}^{N}$, Nonlinearity, 19 (2006), 2169-2191.
doi: 10.1088/0951-7715/19/9/011. |
[5] |
L. C. F. Ferreira and E. J. Villamizar-Roa, On the stability problem for the Boussinesq equations in weak-$L^p$ spaces, Communication on Pure and Applied Analysis, 9 (2010), 667-684.
doi: 10.3934/cpaa.2010.9.667. |
[6] |
G. Galdi, "An Introduction to the Mathematical Theory of the Navier-Stokes Equations," Vol. II. Nonlinear Steady Problems, Springer Tracts in Natural Nature Philosophy, 39, Springer-Verlag, New York, 1994. |
[7] |
G. Galdi, On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, Handbook of Mathematical fluid dynamics, Vol. I 653-791, North-Holland, Amsterdam (2002), 653-791. |
[8] |
G. Galdi and A. Silvestre, Strong solutions to the Navier-Stokes equations around a rotating obstacle, Arch. Rational Mech. Anal., 176 (2005), 331-350.
doi: 10.1007/s00205-004-0348-z. |
[9] |
G. Galdi and A. Silvestre, Existence of time-periodic solutions to the Navier-Stokes equations around a moving body, Pacific Journal of Mathematics, 223 (2006), 251-267.
doi: 10.2140/pjm.2006.223.251. |
[10] |
J. Heywood, The Navier-Stokes Equations: On the existence, regularity and decay of solutions, Indiana Univ. Math. Journal, 29 (1980), 639-681.
doi: 10.1512/iumj.1980.29.29048. |
[11] |
T. Hishida, An existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle, Arch. Rat. Mech. Anal., 150 (1999), 307-348.
doi: 10.1007/s002050050190. |
[12] |
J. L. Lions and E. Magenes, "Problèmes aux Limites Non Homogènes et Applications," vol. 1, Travaux et Recherches Mathéatiques, No. 17 Dunod, Paris 1968. |
[13] |
L. D. Landau and E. M. Lifchitz, "Theorical Physics: Fluid Mechanics," 2nd edition, Pergamon Press, 1987. |
[14] |
M. A. Rojas-Medar and S. A. Lorca, The equations of a viscous incompressible chemical active fluid II. Regularity of solutions, Rev. Mat. Apl., 16 (1995), 81-95. |
show all references
References:
[1] |
J. Bergh and J. Löfström, "Interpolation Spaces. An Introduction," Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. |
[2] |
J. L. Boldrini and S. Lorca, The initial value problem for a generalized Boussinesq model, Nonlinear Analysis, 36 (1999), 457-480.
doi: 10.1016/S0362-546X(97)00635-4. |
[3] |
P. Braz e Silva, M. A. Rojas-Medar and E. J. Villamizar-Roa, Strong solutions for the nonhomogeneous Navier-Stokes equations in unbounded domains, Math. Methods Appl. Sci., 33 (2010), 358-372. |
[4] |
L. C. F. Ferreira and E. J. Villamizar-Roa, Well-posedness and asymptotic behaviour for the convection problem in $\mathbb{R}^{N}$, Nonlinearity, 19 (2006), 2169-2191.
doi: 10.1088/0951-7715/19/9/011. |
[5] |
L. C. F. Ferreira and E. J. Villamizar-Roa, On the stability problem for the Boussinesq equations in weak-$L^p$ spaces, Communication on Pure and Applied Analysis, 9 (2010), 667-684.
doi: 10.3934/cpaa.2010.9.667. |
[6] |
G. Galdi, "An Introduction to the Mathematical Theory of the Navier-Stokes Equations," Vol. II. Nonlinear Steady Problems, Springer Tracts in Natural Nature Philosophy, 39, Springer-Verlag, New York, 1994. |
[7] |
G. Galdi, On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, Handbook of Mathematical fluid dynamics, Vol. I 653-791, North-Holland, Amsterdam (2002), 653-791. |
[8] |
G. Galdi and A. Silvestre, Strong solutions to the Navier-Stokes equations around a rotating obstacle, Arch. Rational Mech. Anal., 176 (2005), 331-350.
doi: 10.1007/s00205-004-0348-z. |
[9] |
G. Galdi and A. Silvestre, Existence of time-periodic solutions to the Navier-Stokes equations around a moving body, Pacific Journal of Mathematics, 223 (2006), 251-267.
doi: 10.2140/pjm.2006.223.251. |
[10] |
J. Heywood, The Navier-Stokes Equations: On the existence, regularity and decay of solutions, Indiana Univ. Math. Journal, 29 (1980), 639-681.
doi: 10.1512/iumj.1980.29.29048. |
[11] |
T. Hishida, An existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle, Arch. Rat. Mech. Anal., 150 (1999), 307-348.
doi: 10.1007/s002050050190. |
[12] |
J. L. Lions and E. Magenes, "Problèmes aux Limites Non Homogènes et Applications," vol. 1, Travaux et Recherches Mathéatiques, No. 17 Dunod, Paris 1968. |
[13] |
L. D. Landau and E. M. Lifchitz, "Theorical Physics: Fluid Mechanics," 2nd edition, Pergamon Press, 1987. |
[14] |
M. A. Rojas-Medar and S. A. Lorca, The equations of a viscous incompressible chemical active fluid II. Regularity of solutions, Rev. Mat. Apl., 16 (1995), 81-95. |
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