Computation for the canonical measures of a colored disordered lattice gas and spectral gap
In this work we deal with spectral gap and canonical measures related to a model called colored disordered lattice gas. We consider the approach used in the work of Dermoune and Heinrich [“A sma...
In this work we deal with spectral gap and canonical measures related to a model called colored disordered lattice gas. We consider the approach used in the work of Dermoune and Heinrich [“A sma...
Quantum hypothesis testing with group symmetry
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymp...
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymp...
Nonlinear stability of boundary layer solution to the Boltzmann equation with diffusive effect at the boundary
J. Math. Phys. 50, 103303 (2009); doi:10.1063/1.3220562
Published 8 October 2009
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In this paper, the stability of boundary layer solutions to the Boltzmann equation with diffusive effect at the boundary for hard sphere model is considered. When the Mach number of the far field is less than −1, the exponential decay in time is proven for linearized operator first. At last, based on this property, nonlinear stability of the boundary layers is obtained by bootstrap argument.
©2009 American Institute of Physics
| History: | Received 10 June 2009; accepted 9 August 2009; published 8 October 2009 |
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- Bardos, C., Caflish, R. E., and Nicolaenko, B., “The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas,”
Commun. Pure Appl. Math. 39, 323 (1986) . - Bardos, C., Golse, F., and Sone, Y., “Half-space problems for the Boltzmann equation: A survey,”
J. Stat. Phys. 124, 275 (2006) . - Carleman, T., “Sur La théorie de l'équation intégrodifférentielle de Boltzmann,”
Acta Math. 60, 91 (1933) . - Cercignani, C., Illner, R., and Pulvirenti, M., The Mathematical Theory of Dilute Gases (Springer-Verlag, Berlin, 1994).
- Chen, C. C., Liu, T. P., and Yang, T., “Existence of boundary layer solutions to the Boltzmann equation,”
Analysis and Applications 2, 337 (2004) . - Coron, F., Golse, F., and Sulem, C., “A classification of well-posed kinetic layer problems,”
Commun. Pure Appl. Math. 41, 409 (1988) . - Glassey, R. T., The Cauchy Problem in Kinetic Theory (SIAM, Philadelphia, 1996).
- Golse, F., Perthame, B., and Sulem, C., “On a boundary layer problem for the nonlinear Boltzmann equation,”
Arch. Ration. Mech. Anal. 103, 81 (1988) . - Golse, F. and Poupaud, F., “Stationary solutions of the linearized Boltzmann equation in a half-space,”
Math. Methods Appl. Sci. 11, 483 (1989) . - Kawashima, S., and Nishibata, S., “Existence of a stationary wave for the discrete Boltzmann equation in the half space,”
Commun. Math. Phys. 207, 385 (1999) . - Kawashima, S. and Nishibata, S., “Stationary waves for the discrete Boltzmann equation in the half space with reflective boundaries,”
Commun. Math. Phys. 211, 183 (2000) . - Nikkuni, Y. and Kawashima, S., “Stability of stationary solutions to the half-space problem for the discrete Boltzmann equation with multiple collisions,”
Kyushu Journal of Mathematics 54, 233 (2000) . - Sone, Y., Kinetic Theory and Fluid Dynamics (Birkhäuser, Berlin, 2002).
- Tian, Q. Z., “Existence of nonlinear boundary layer solution to the Boltzmann equation with physical boundary conditions,”
J. Math. Anal. Appl. 356, 42 (2009) . - Ukai, S., Yang, T., and Yu, S. H., “Nonlinear boundary layers of the Boltzmann equation: I. Existence,”
Commun. Math. Phys. 236, 373 (2003) . - Ukai, S., Yang, T., and Yu, S. H., “Nonlinear stability of boundary layers of the Boltzmann equation. I. The case
<−1,”
Commun. Math. Phys. 244, 99 (2004) . - Ukai, S., Yang, T., and Zhao, H. J., “Stationary solutions to the exterior problems for the Boltzmann equation. I. Existence,”
Discrete Contin. Dyn. Syst. 23, 495 (2009) . - Wang, W. K., Yang, T., and Yang, X. F., “Nonlinear stability of boundary layers of the Boltzmann equation for cutoff hard potentials,” J. Math. Phys. 47, 083301 (2006).
- Wang, W. K., Yang, T., and Yang, X. F., “Existence of boundary layers to the Boltzmann equation with cutoff soft potentials,” J. Math. Phys. 48, 073304 (2007).
- Yang, T. and Zhao, H. J., “A half-space problem for the Boltzmann equation with specular reflection boundary condition,”
Commun. Math. Phys. 255, 683 (2005) . - Yang, X. F., “Nonlinear stability of boundary layers for the Boltzmann equation with cutoff soft potentials,”
J. Math. Anal. Appl. 345, 941 (2008) .
