HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM

Volume: 9 Number: 3 September 1, 2019
  • F. Ben Belgacem
EN

HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM

Abstract

This paper investigates the hydrodynamic limit of the Boltzmann-Monge-Ampere system in the so-called quasineutral regime and more precisely the convergence of the Boltzmann-Monge-Ampere system to the Euler equation by using the relative entropy method.

Keywords

References

  1. Brenier, Y. (1991),Polar factorization and monotone rearrangement of vector-valued functions, Pure Appl. Math., 44, (4), pp. 375-417.
  2. Brenier, Y. and Gr´egoire, L. (2004) , A geometric approximation to the Euler equations: the Vlasov- Monge-Amp`ere system, Geom. Funct. Anal. 14, pp. 1182-1218.
  3. Caffarelli, L. (1990), Interior W2,pestimates for solutions of Monge-Amp`ere equation, Ann. Math. 131 (1) pp. 135-150.
  4. Cercignani, C. (1988), The Boltzmann equation and its applications, Applied Mathematical Sciences, 67. Springer, New York.
  5. Cercignani, C., Illner, R., and Pulvirenti, M. (1994), The mathematical theory of dilute gases, Applied Mathematical Sciences, 106, Springer, New York.
  6. DiPerna, R. J., Lions, P. L. (1989), On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math., 130, pp. 321-366.
  7. DiPerna, R. J., Lions, P. L. (1989), Global weak solution of Vlasov-Maxwell systems, Comm. Pure Appl. Math., 42, pp. 729-757.
  8. Desvillettes, L., Dolbeault, J. (1991), On long time asymptotics of the Vlasov-Poisson-Boltzmann equation, Comm. Partial Differential Equations, 16, pp. 451-489.

Details

Primary Language

English

Subjects

-

Journal Section

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Authors

F. Ben Belgacem This is me

Publication Date

September 1, 2019

Submission Date

-

Acceptance Date

-

Published in Issue

Year 2019 Volume: 9 Number: 3

APA
Belgacem, F. B. (2019). HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM. TWMS Journal of Applied and Engineering Mathematics, 9(3), 493-499. https://izlik.org/JA23WZ73EB
AMA
1.Belgacem FB. HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM. JAEM. 2019;9(3):493-499. https://izlik.org/JA23WZ73EB
Chicago
Belgacem, F. Ben. 2019. “HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM”. TWMS Journal of Applied and Engineering Mathematics 9 (3): 493-99. https://izlik.org/JA23WZ73EB.
EndNote
Belgacem FB (September 1, 2019) HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM. TWMS Journal of Applied and Engineering Mathematics 9 3 493–499.
IEEE
[1]F. B. Belgacem, “HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM”, JAEM, vol. 9, no. 3, pp. 493–499, Sept. 2019, [Online]. Available: https://izlik.org/JA23WZ73EB
ISNAD
Belgacem, F. Ben. “HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM”. TWMS Journal of Applied and Engineering Mathematics 9/3 (September 1, 2019): 493-499. https://izlik.org/JA23WZ73EB.
JAMA
1.Belgacem FB. HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM. JAEM. 2019;9:493–499.
MLA
Belgacem, F. Ben. “HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM”. TWMS Journal of Applied and Engineering Mathematics, vol. 9, no. 3, Sept. 2019, pp. 493-9, https://izlik.org/JA23WZ73EB.
Vancouver
1.F. Ben Belgacem. HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM. JAEM [Internet]. 2019 Sep. 1;9(3):493-9. Available from: https://izlik.org/JA23WZ73EB