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Numerical study of a family of dissipative KdV equations
Resolvent estimates for a two-dimensional non-self-adjoint operator
1. | Institut de Mathématiques de Jussieu, Université Pierre-et-Marie-Curie (Paris 6), 4 place Jussieu, 75005 Paris, France |
References:
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N. Dencker, J. Sjöstrand and M. Zworski, Pseudospectra of semiclassical (pseudo-) differential operators, Comm. Pure Appl. Math., 57 (2004), 384-415.
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I. Gallagher, T. Gallay and F. Nier, Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator, Int. Math. Res. Not. IMRN, 12 (2009), 2147-2199.
doi: 10.1002/cpa.20004. |
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T. Gallay and C. E. Wayne, Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on $R^2$, Arch. Ration. Mech. Anal., 163 (2002), 209-258.
doi: 10.1007/s002050200200. |
[4] |
T. Gallay and C. E. Wayne, Global stability of vortex solutions of the two-dimensional Navier-Stokes equation, Comm. Math. Phys., 225 (2005), 97-129.
doi: 10.1007/s00220-004-1254-9. |
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L. Hörmander, "The Analysis of Linear Partial Differential Operators. I," Springer-Verlag, Berlin, 1983.
doi: 10.1007/978-3-642-96750-4. |
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L. Hörmander, "The Analysis of Linear Partial Differential Operators. III," Springer-Verlag, Berlin, 1985. |
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T. Kato, "Perturbation Theory for Linear Operators," Springer-Verlag, Berlin, 1995. |
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N. Lerner, "Metrics on the Phase Space and Non-selfadjoint Pseudo-differential Operators," Birkhäuser Verlag, Basel, 2010.
doi: 10.1007/978-3-7643-8510-1. |
[9] |
K. Pravda-Starov, A general result about the pseudo-spectrum of Schrödinger operators, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 460 (2004), 471-477.
doi: 10.1098/rspa.2003.1194. |
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L. N. Trefethen, Pseudospectra of linear operators, SIAM Rev., 39 (1997), 383-406.
doi: 10.1137/S0036144595295284. |
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L. N. Trefethen and M. Embree, "Spectra and Pseudospectra," Princeton University Press, Princeton, NJ, 2005. |
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C. Villani, Hypocoercive diffusion operators, International Congress of Mathematicians. Vol. III (2006), 473-498. |
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C. Villani, Hypocoercivity, Mem. Amer. Math. Soc., 202 (2009).
doi: 10.1090/S0065-9266-09-00567-5. |
show all references
References:
[1] |
N. Dencker, J. Sjöstrand and M. Zworski, Pseudospectra of semiclassical (pseudo-) differential operators, Comm. Pure Appl. Math., 57 (2004), 384-415.
doi: 10.1002/cpa.20004. |
[2] |
I. Gallagher, T. Gallay and F. Nier, Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator, Int. Math. Res. Not. IMRN, 12 (2009), 2147-2199.
doi: 10.1002/cpa.20004. |
[3] |
T. Gallay and C. E. Wayne, Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on $R^2$, Arch. Ration. Mech. Anal., 163 (2002), 209-258.
doi: 10.1007/s002050200200. |
[4] |
T. Gallay and C. E. Wayne, Global stability of vortex solutions of the two-dimensional Navier-Stokes equation, Comm. Math. Phys., 225 (2005), 97-129.
doi: 10.1007/s00220-004-1254-9. |
[5] |
L. Hörmander, "The Analysis of Linear Partial Differential Operators. I," Springer-Verlag, Berlin, 1983.
doi: 10.1007/978-3-642-96750-4. |
[6] |
L. Hörmander, "The Analysis of Linear Partial Differential Operators. III," Springer-Verlag, Berlin, 1985. |
[7] |
T. Kato, "Perturbation Theory for Linear Operators," Springer-Verlag, Berlin, 1995. |
[8] |
N. Lerner, "Metrics on the Phase Space and Non-selfadjoint Pseudo-differential Operators," Birkhäuser Verlag, Basel, 2010.
doi: 10.1007/978-3-7643-8510-1. |
[9] |
K. Pravda-Starov, A general result about the pseudo-spectrum of Schrödinger operators, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 460 (2004), 471-477.
doi: 10.1098/rspa.2003.1194. |
[10] |
L. N. Trefethen, Pseudospectra of linear operators, SIAM Rev., 39 (1997), 383-406.
doi: 10.1137/S0036144595295284. |
[11] |
L. N. Trefethen and M. Embree, "Spectra and Pseudospectra," Princeton University Press, Princeton, NJ, 2005. |
[12] |
C. Villani, Hypocoercive diffusion operators, International Congress of Mathematicians. Vol. III (2006), 473-498. |
[13] |
C. Villani, Hypocoercivity, Mem. Amer. Math. Soc., 202 (2009).
doi: 10.1090/S0065-9266-09-00567-5. |
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