Abstract
In this paper, we consider the Cauchy problem for the relativistic Enskog equation with near vacuum data for a hard sphere gas in the Robertson–Walker space-time. We prove an existence and uniqueness result of the global (in time) mild solution in a suitable weighted space. We also study the asymptotic behavior of the solution as well as the
References
[1] L. Arkeryd, On the Enskog equation with large initial data, SIAM J. Math. Anal. 21 (1990), no. 3, 631–646. 10.1137/0521033Search in Google Scholar
[2] L. Arkeryd and C. Cercignani, On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation, Comm. Partial Differential Equations 14 (1989), no. 8–9, 1071–1089. 10.1080/03605308908820644Search in Google Scholar
[3] C. Cercignani, Existence of global solutions for the space inhomogeneous Enskog equation, Transp. Theory Stat. Phys. 16 (1987), 213–221. 10.1080/00411458708204660Search in Google Scholar
[4]
C. Cercignani,
Small data existence for the Enskog equation in
[5] D. Enskog, Kinetiche theorie, Kgl. Svenska Vet. Akad. Handl. 63 (1921), no. 4, 3–44; translation in Kinetic Theory, Vol. 3, Pergamon, New York, 1972. Search in Google Scholar
[6] R. Galeano Andrades, B. Orozco Herrera and M. O. Vasquez Avila, The relativistic Enskog equation near the vacuum, Electron. J. Differ. Equ. Conf. 2005 (2005), no. 13, 21–27. Search in Google Scholar
[7] R. T. Glassey, Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data, Comm. Math. Phys. 264 (2006), no. 3, 705–724. 10.1007/s00220-006-1522-ySearch in Google Scholar
[8] J. Huang and Z. Jiang, Uniform stability of the solutions to the relativistic Enskog equation, J. Math. Anal. Appl. 446 (2017), no. 1, 411–425. 10.1016/j.jmaa.2016.08.059Search in Google Scholar
[9] Z. Jiang, Global solution to the relativistic Enskog equation with near-vacuum data, J. Stat. Phys. 127 (2007), no. 4, 805–812. 10.1007/s10955-006-9269-6Search in Google Scholar
[10] M. A. Lachowicz, On the local existence and uniqueness of solution of initial value problem for the Enskog equation, Bull. Pol. Acad. Sci. Math. 31 (1983), no. 1–2, 89–97. Search in Google Scholar
[11] H. Lee, Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson–Walker spacetime, J. Differential Equations 255 (2013), no. 11, 4267–4288. 10.1016/j.jde.2013.08.006Search in Google Scholar
[12] H. Lee and A. D. Rendall, The spatially homogeneous relativistic Boltzmann equation with a hard potential, Comm. Partial Differential Equations 38 (2013), no. 12, 2238–2262. 10.1080/03605302.2013.827709Search in Google Scholar
[13]
J. Polewczak,
Global existence in
[14] R. M. Strain, Global Newtonian limit for the relativistic Boltzmann equation near vacuum, SIAM J. Math. Anal. 42 (2010), no. 4, 1568–1601. 10.1137/090762695Search in Google Scholar
[15] E. Takou and F. L. Ciake Ciake, Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson–Walker space-time, Ann. Inst. Fourier (Grenoble) 67 (2017), no. 3, 947–967. 10.5802/aif.3101Search in Google Scholar
[16] C. Villani, Mathematics of granular materials, J. Stat. Phys. 124 (2006), no. 2–4, 781–822. 10.1007/s10955-006-9038-6Search in Google Scholar
[17] Z. Wu, Stability of global solution for the relativistic Enskog equation near vacuum, J. Stat. Phys. 137 (2009), no. 1, 149–164. 10.1007/s10955-009-9848-4Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Meromorphic function sharing a small function with a homogeneous differential polynomial
- On generalized quasi-Einstein manifolds
- On Green’s function of the Robin problem for the Poisson equation
- Moment functions on hypergroup joins
- Sparse reconstruction with multiple Walsh matrices
- On certain equations in semiprime rings and standard operator algebras
- Derivatives of meromorphic functions sharing two sets with least cardinalities
- The metric derivative of set-valued functions
- The relativistic Enskog equation near the vacuum in the Robertson–Walker space-time
Articles in the same Issue
- Frontmatter
- Meromorphic function sharing a small function with a homogeneous differential polynomial
- On generalized quasi-Einstein manifolds
- On Green’s function of the Robin problem for the Poisson equation
- Moment functions on hypergroup joins
- Sparse reconstruction with multiple Walsh matrices
- On certain equations in semiprime rings and standard operator algebras
- Derivatives of meromorphic functions sharing two sets with least cardinalities
- The metric derivative of set-valued functions
- The relativistic Enskog equation near the vacuum in the Robertson–Walker space-time