2000 character limit reached
Quantitative relaxation towards equilibrium for solutions to the Boltzmann-Fermi-Dirac equation with cutoff hard potentials
Published 9 Feb 2024 in math.AP, math-ph, and math.MP | (2402.06807v1)
Abstract: We provide the first quantitative result of convergence to equilibrium in the context of the spatially homogeneous Boltzmann-Fermi-Dirac equation associated to hard potentials interactions under angular cut-off assumption, providing an explicit - algebraic - rate of convergence to Fermi-Dirac steady solutions. This result complements the quantitative convergence result of Liu and Lu and is based upon new uniform-in-time-and-$\varepsilon$ $L{\infty}$ bound on the solutions.
- About the Landau-Fermi-Dirac equation with moderately soft potentials. Arch. Ration. Mech. Anal., 244(3):779–875, 2022.
- Long time dynamics for the Landau-Fermi-Dirac equation with hard potentials. J. Differential Equations, 270:596–663, 2021.
- R. J. Alonso and E. Carneiro. Estimates for the boltzmann collision operator via radial symmetry and fourier transform. Advances in Mathematics, 223(2):511–528, 2010.
- Convolution inequalities for the Boltzmann collision operator. Comm. Math. Phys., 298(2):293–322, 2010.
- The Boltzmann equation for hard potentials with integrable angular transition: Coerciveness, exponential tails rates, and Lebesgue integrability. arXiv preprint arXiv:2211.09188, 2022.
- Exponentially-tailed regularity and time asymptotic for the homogeneous boltzmann equation. arXiv preprint arXiv:1711.06596, 2017.
- T. Borsoni. Extending Cercignani’s conjecture results from botzmann to boltzmann-fermi-dirac equation. arXiv preprint arXiv:2304.11956, 2023.
- Entropy production estimates for Boltzmann equations with physically realistic collision kernels. J. Statist. Phys., 74(3-4):743–782, 1994.
- C. Cercignani. H𝐻Hitalic_H-theorem and trend to equilibrium in the kinetic theory of gases. Arch. Mech. (Arch. Mech. Stos.), 34(3):231–241 (1983), 1982.
- S. Chapman and T. G. Cowling. The Mathematical Theory of Non-uniform Gases. Cambridge University Press, Cambridge, 1939.
- J. Dolbeault. Kinetic models and quantum effects: a modified Boltzmann equation for Fermi-Dirac particles. Arch. Rational Mech. Anal., 127(2):101–131, 1994.
- Factorization of non-symmetric operators and exponential H𝐻Hitalic_H-theorem. Mém. Soc. Math. Fr. (N.S.), (153):137, 2017.
- On semi-classical limit of spatially homogeneous quantum Boltzmann equation: weak convergence. Comm. Math. Phys., 386(1):143–223, 2021.
- E. H. Lieb. Sharp constants in the Hardy-Littelwood-Sobolev and related inequalities. In Inequalities: Selecta of Elliott H. Lieb, pages 529–554. Springer, 1983.
- B. Liu and X. Lu. On the convergence to equilibrium for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. J. Stat. Phys., 190(8):Paper No. 139, 36, 2023.
- X. Lu. On spatially homogeneous solutions of a modified Boltzmann equation for Fermi-Dirac particles. J. Statist. Phys., 105(1-2):353–388, 2001.
- X. Lu and B. Wennberg. On stability and strong convergence for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Arch. Ration. Mech. Anal., 168(1):1–34, 2003.
- Clément M. Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. Comm. Math. Phys., 261(3):629–672, 2006.
- A. Pulvirenti and B. Wennberg. A Maxwellian lower bound for solutions to the Boltzmann equation. Comm. Math. Phys., 183(1):145–160, 1997.
- G. Toscani and C. Villani. Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Comm. Math. Phys., 203(3):667–706, 1999.
- C. Villani. Cercignani’s conjecture is sometimes true and always almost true. Comm. Math. Phys., 234(3):455–490, 2003.
- J. Wang and L. Ren. Global existence and stability of solutions of spatially homogeneous Boltzmann equation for Fermi-Dirac particles. J. Funct. Anal., 284(1):Paper No. 109737, 91, 2023.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.