본문 바로가기
KERD
논문KCI 등재

A REGULARITY CONDITION FOR THE DENSITY-DEPENDENT MAGNETOHYDRODYNAMIC EQUATIONS IN BMO SPACE

Zujin Zhang|Xian Yang|SHULIN QIU
장전수학회 (Jangjeon Mathematical Society)|2016.01|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제19권 제1호|pp. 125-134|DOI 10.17777/pjms.2016.19.1.013

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Density-dependent MHD equationsDensity-dependent Hall-MHD systemRegularity criterionBMO space
주제분류수학

초록

In this paper, we consider the density-dependent magnetohydrodynamic equations, and provide a regularity criterion involving the velocity field in BMO space, which extends [J.S. Fan, F.C.Li, G. Nakamura, Z. Tan, Regularity criteria for the three-dimensional magnetohydrodynamic equations, J. Differential Equations, 256 (2014), 2858-2875]. Moreover, we applied our method of proof to the density-dependent Hall-MHD system.

Abstract

In this paper, we consider the density-dependent magnetohydrodynamic equations, and provide a regularity criterion involving the velocity field in BMO space, which extends [J.S. Fan, F.C.Li, G. Nakamura, Z. Tan, Regularity criteria for the three-dimensional magnetohydrodynamic equations, J. Differential Equations, 256 (2014), 2858-2875]. Moreover, we applied our method of proof to the density-dependent Hall-MHD system.

참고문헌 (27)

  1. H. Abidi, "Resultats d'exstence dans des espaces critiques pour le systeme de la MHD inhomogene", Ann. Math. Blaise Pascal, 14, pp.103~148 (2007)
  2. H. Abidi, "Global existence for the magnetohydrodynamic sytsem in critical spaces", Proc. Roy. Soc. Edinburgh, Sect. A, 138, pp.447~476 (2008)
  3. M. Acheritogaray, "Kinetic formulation and global existence for the Hall-Magento-hydrodynmics systems", Kinet. Relat. Models, 4, pp.901~918 (2011)
  4. S.A. Balbus, "Linear Analysis of the Hall effect in protosteller disks", Astrophys. J, 552, pp.235~247 (2001)
  5. L.M.B.C. Campos, "On hydromagnetic waves in atmospheres with application to the sun", Theor. Comput. Fluid Dyn, 10, pp.37~70 (1998)
  6. D. Chae, "Well-posedness for Hall-magnetohydrodynamics", Ann. I. H. Poincare-AN, 31, pp.555~565 (2014)
  7. D. Chae, "On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics", J. Differential Equations, 256, pp.3835~3858 (2014)
  8. D. Chae, "On the temporal decay for the Hall-magnetohydrodynamic equations", J. Differential Equations, 255, pp.3971~3982 (2013)
  9. J. Bergh, "Grundlehren Math. Wiss", pp.223~ (1976), Springer-Verlag
  10. Q. Chen, "Strong solutions to the incompressible magnetohydrodynamic equations", Math. Methods Appl. Sci, 34, pp.94~107 (2011)
  11. B. Desjardins, "Remarks on a nonhomogeneous model of magnetohydrodynamics", Differential Integral Equations, 11, pp.377~394 (1998)
  12. J.S. Fan, "Regularity criteria for the three-dimensional magnetohydrodynamic equations", J. Differential Equations, 256, pp.2858~2875 (2014)
  13. J.S. Fan, "Regularity criteria for the density-dependent Hallmagnetohydrodynamics", Appl. Math. Lett, 36, pp.14~18 (2014)
  14. T.G. Forbes, "Magnetic reconnection in solar ares", Geophys. Astrophys. Fluid Dyn, 62, pp.15~36 (1991)
  15. J.F. Berbeau, "Existence of solution for a density-dependent magnetohydrodynamic equation", Adv. Differential Equations, 2, pp.427~452 (1997)
  16. H. Homann, "Bifurcation analysis of magnetic reconnection in Hall-MHD sytsems", Phys. D, 208, pp.59~72 (2005)
  17. M.J. Lighthill, "Studies on magneto-hydrodynamic waves and other anisotropic wave motions", Philos. Trans. R. Soc. Lond. Ser. A, 252, pp.397~430 (1960)
  18. S. Machihara, "Interpolation inequalities in Besov spaces", Proceedings of the American Mathematical Society, 131, pp.1553~1556 (2002)
  19. P.D. Minini, "Dynamo action in magnetohydrodynamics and Hall magnetohydrodynamics", Astrophys, 587, pp.472~481 (2003)
  20. D.A. Shalybkov, "The Hall effect and the decay of magnetic fields", Astron. Astrophys, 321, pp.685~690 (1997)
  21. R.S. Strichartz, "Bounded mean oscillation and Sobolev sapces", Indiana Univ. Math. J, 29, pp.539~558 (1980)
  22. D.A. Shalybkov, "The Hall effect and the decay of magnetic fields", Astron. Astrophys, 321, pp.685~690 (1997)
  23. M. Wardle, "Star formation and the Hall effect", Astrophys. Space Sci, 292, pp.317~323 (2004)
  24. R. Temam, "theory and numercial analysis" (2001), AMS chelsea Publishing
  25. H. Triebel, "Theory of function spaces" (1983), Birkhauser-Verlag
  26. H. Wu, "Strong solution to the incompressible MHD equations with vacuum", Comput. Math. Appl, 61, pp.2742~2753 (2011)
  27. Y. Zhou, "A regularity criterion for the density-dependent magnetohydrodynamic equations", Math. Meth. Appl. Sci, 33, pp.1350~1355 (2010)

관련 논문AI추천

REMARKS ON LOGARITHMICALLY REGULARITY CRITERIA FOR THE 3D VISCOUS MHD EQUATIONSSadek Gala, Xiaochun Chen대한수학회 · 대한수학회지2011 · 제48권 제3호Global large solutions for the compressible magnetohydrodynamic systemJinlu Li, Weipeng Zhu, Yanghai Yu대한수학회 · 대한수학회보2021 · 제58권 제6호Asymptotic behavior of solutions for the generalized MHD and Hall-MHD systems in $\mathbb{R}^n$Mingxuan Zhu대한수학회 · 대한수학회보2018 · 제55권 제3호Remarks on Liouville type theorems for the 3D stationary MHD equationsPan Liu, Pengcheng Niu, Zhouyu Li대한수학회 · 대한수학회보2020 · 제57권 제5호The quasi-neutral limit of the compressible magnetohydrodynamic flows for ionic dynamics권영삼대한수학회 · 대한수학회지2019 · 제56권 제6호The 3D Boussinesq equations with regularity in the horizontal component of the velocityQiao Liu대한수학회 · 대한수학회보2020 · 제57권 제3호

이 간행물의 다른 논문 (18건)

SYMMETRIC IDENTITIES OF DEGENERATE q-BERNOULLI POLYNOMIALS UNDER SYMMETRY GROUP S3권혁인, Dmitry V. Dolgy, 김태균, 서종진pp. 1-9A disproval of a conjecture concerning the Rademacher pseudocharacter on SL(2, Z)A. I. Shternpp. 11-16NEW APPROACH TO THE SIGN PATTERNS THAT REQUIRE POWER NONNEGATIVITY, OR REQUIRE EVENTUAL NONNEGATIVITY박진우pp. 17-27Analysis of TPMACA with two trees based on 90/150 TPSACA최언숙, 공길탁, 조성진pp. 29-38SOME IDENTITIES INVOLVING FROBENIUS-EULER POLYNOMIALS AND NUMBERS김태균, 서종진pp. 39-46
원문 보기