Hydrodynamic limits : some improvements of the relative entropy method
Annales de l'I.H.P. Analyse non linéaire (2009)
- Volume: 26, Issue: 3, page 705-744
- ISSN: 0294-1449
Access Full Article
topHow to cite
topReferences
top- [1] Aoki K., Sone Y., Steady gas flows past bodies at small Knudsen numbers – Boltzmann and hydrodynamic systems, Trans. Theory Stat. Phys.16 (1987) 189-199. Zbl0622.76082
- [2] Bardos C., Golse F., Levermore C.D., Fluid dynamic limits of the Boltzmann equation I, J. Stat. Phys.63 (1991) 323-344. Zbl0918.35109MR1115587
- [3] Bardos C., Golse F., Levermore C.D., Fluid dynamic limits of the Boltzmann equation II: Convergence proofs, Comm. Pure Appl. Math.46 (1993) 667-753. Zbl0817.76002MR1213991
- [4] Biryuk A., Craig W., Panferov V., Strong solutions of the Boltzmann equation in one spatial dimension, C. R. Acad. Sci. Paris342 (2006) 843-848. Zbl1096.35001MR2224633
- [5] Bouchut F., Golse F., Pulvirenti M., Desvillettes L., Perthame B. (Eds.), Kinetic Equations and Asymptotic Theory, Editions scientifiques et médicales Elsevier, Paris, 2000. MR2065070
- [6] Caflisch R., The Boltzmann equation with a soft potential. I. Linear, spatially-homogeneous, Commun. Math. Phys.74 (1980) 71-95. Zbl0434.76065MR575897
- [7] Cercignani C., Global weak solutions of the Boltzmann equation, J. Stat. Phys.118 (2005) 333-342. Zbl1097.82022MR2122558
- [8] Chapman S., Cowling T.G., The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction, and Diffusion in Gases, Cambridge University Press, New York, 1960. Zbl0726.76084MR116537JFM65.1541.01
- [9] Chemin J.-Y., Perfect Incompressible Fluids, Oxford Lecture Series in Mathematics and its Applications, vol. 14, The Clarendon Press, Oxford University Press, New York, 1998. Zbl0927.76002MR1688875
- [10] Chemin J.-Y., Desjardins B., Gallagher I., Grenier E., Mathematical Geophysics. An Introduction to Rotating Fluids and the Navier–Stokes Equations, Oxford Lecture Series in Mathematics and its Applications, vol. 32, The Clarendon Press, Oxford University Press, Oxford, 2006. Zbl1205.86001MR2228849
- [11] DeMasi A., Esposito R., Lebowitz J., Incompressible Navier–Stokes and Euler limits of the Boltzmann equation, Comm Pure Appl. Math.42 (1990) 1189-1214. Zbl0689.76024MR1029125
- [12] Desjardins B., Grenier E., Low Mach number limit of viscous compressible flows in the whole space, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci.455 (1999) 2271-2279. Zbl0934.76080MR1702718
- [13] Di Perna R., Lions P.-L., On the Cauchy problem for the Boltzmann equation: global existence and weak stability results, Ann. of Math.130 (1990) 321-366. Zbl0698.45010MR1014927
- [14] Gallagher I., Saint-Raymond L., On the influence of the Earth's rotation on geophysical flows, in: Handbook of Mathematical Fluid Dynamics, vol. 4, Elsevier, 2007.
- [15] F. Golse, L. Saint-Raymond, The Navier–Stokes limit of the Boltzmann equation for hard potentials, submitted for publication. Zbl1178.35290
- [16] H. Grad, Asymptotic theory of the Boltzmann equation. II, in: Rarefied Gas Dynamics, vol. I, Proc. 3rd Internat. Sympos., Palais de l'UNESCO, Paris, 1962, 1963, pp. 26–59. MR156656
- [17] Grenier E., Quelques Limites Singulières Oscillantes, Séminaire sur les Equations aux Dérivées Partielles, vol. 21, Ecole Polytech., Palaiseau, 1995. Zbl0873.35068MR1362569
- [18] Grenier E., On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math.53 (2000) 1067-1091. Zbl1048.35081MR1761409
- [19] Guo Y., The Vlasov–Poisson–Boltzmann system near Maxwellians, Comm. Pure Appl. Math.55 (2002) 1104-1135. Zbl1027.82035MR1908664
- [20] Guo Y., The Boltzmann equation in the whole space, Indiana Univ. Math. J.53 (2004) 1081-1094. Zbl1065.35090MR2095473
- [21] Hilbert D., Begründung der kinetischen Gastheorie, Math. Ann.72 (1912) 562-577. Zbl43.1055.03MR1511713JFM43.1055.03
- [22] Lions P.-L., Conditions at infinity for Boltzmann's equation, Comm. Partial Differential Equations19 (1994) 335-367. Zbl0799.35210MR1257008
- [23] Lions P.-L., Masmoudi N., From Boltzmann equation to the Navier–Stokes and Euler equations I, Arch. Ration Mech. Anal.158 (2001) 173-193. Zbl0987.76088MR1842343
- [24] Lions P.-L., Masmoudi N., Une approche locale de la limite incompressible, C. R. Acad. Sci. Paris329 (1999) 387-392. Zbl0937.35132MR1710123
- [25] Masmoudi N., Ekman layers of rotating fluids: the case of general initial data, Commun. Pure Appl. Math.53 (2000) 432-483. Zbl1047.76124MR1733696
- [26] S. Mischler, Kinetic equations with Maxwell boundary condition, Preprint. Zbl1228.35249
- [27] Saint-Raymond L., Du modèle BGK de l'équation de Boltzmann aux équations d'Euler des fluides incompressibles, Bull. Sci. Math.126 (2002) 493-506. Zbl1023.76042MR1931626
- [28] Saint-Raymond L., Convergence of solutions to the Boltzmann equation in the incompressible Euler limit, Arch. Ration. Mech. Anal.166 (2003) 47-80. Zbl1016.76071MR1952079
- [29] L. Saint-Raymond, Hydrodynamic limits of the Boltzmann equation, Lectures at SISSA, Trieste, Lecture Notes in Mathematics, Preprint. Zbl1171.82002
- [30] Schochet S., Fast singular limits of hyperbolic PDEs, J. Differential Equations114 (1994) 476-512. Zbl0838.35071MR1303036
- [31] Yau H.T., Relative entropy and hydrodynamics of Ginzburg–Landau models, Lett. Math. Phys.22 (1991) 63-80. Zbl0725.60120MR1121850