본문 바로가기
KERD
논문KCI 등재

Regularity criterion on weak solutions to the Navier-Stokes equations

Sadek Gala
대한수학회 (The Korean Mathematical Society)|2008.03|대한수학회지 (Journal of the KMS)|제45권 제2호|pp. 537-558

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

regularityNavier-Stokes equationsweak solutionmultiplier spaces.
주제분류수학

초록

Consider a weak solution u of the Navier-Stokes equations in the class L² [수식]. We establish a new approach to treat the regularity problem for the Navier-Stokes equation in term of the multiplier space X₁(Rd).

Abstract

Consider a weak solution u of the Navier-Stokes equations in the class L² [수식]. We establish a new approach to treat the regularity problem for the Navier-Stokes equation in term of the multiplier space X₁(Rd).

참고문헌 (20)

  1. H. Beirao da Veiga, "A new regularity class for the Navier-Stokes equations in Rn", Chinese Annals of Mathematics Series B, 16(4), pp.407~412 (1995)
  2. R. Coifman, "Compensated compactness and Hardy spaces", Journal de Mathématiques Pures et Appliquées, 72(3), pp.247~286 (1993)
  3. P. Constantin, "Remarks on the Navier-Stokes Equations, New perspectives in turbulence (Newport, RI, 1989)", pp.229~261 (1991), Springer
  4. C. Foias, "Une remarque sur lunicite des solutions des ´equations de Navier-Stokes en dimension n", Bulletin de la Société Mathématique de France, 89, pp.1~8 (1961)
  5. C. Fefferman, "Hp spaces of several variables", Acta Mathematica, 129(3), pp.137~193 (1972)
  6. E. Hopf, "Uber die Anfangswertaufgabe fur die hydrodynamischen Grundgleichungen", Mathematische Nachrichten, 4, pp.213~231 (1951)
  7. T. Kato, "Strong solutions of the Navier-Stokes equation in Morrey spaces", Boletim da Sociedade Brasileira de Matemática (N.S.), 22(2), pp.127~155 (1992)
  8. H. Kozono, "Regularity criterion of weak solutions to the Navier-Stokes equations", Advances in Differential Equations, 2(4), pp.535~554 (1997)
  9. H. Kozono, "Bilinear estimates in BMO and the Navier-Stokes equations", Mathematische Zeitschrift, 235(1), pp.173~194 (2000)
  10. CRC Research Notes in Mathematics, "Recent Developments in the Navier-Stokes Problem, Chapman & Hall", pp.CRC, P. G. Lemarie-Rieusset
  11. P. G. Lemarie-Rieusset, "Multipliers between Sobolev spaces and fractional differentiation", Journal of Mathematical Analysis and Applications, 322(2), pp.1030~1054 (2006)
  12. J. Leray, "Sur le mouvement d’un liquide visqueux emplissant l’espace", Acta Mathematica, 63(1), pp.193~248 (1934)
  13. F. Murat, "Compacit´e par compensation", Annali della Scuola Normale Superiore di Pisa Classe di Scienze, 5(3), pp.489~507 (1978)
  14. K. Masuda, "Weak solutions of Navier-Stokes equations", Tohoku Mathematical Journal, 36(4), pp.623~646 (1984)
  15. L. Tartar, "Compensated Compactness and Applications to Partial Differential Equations, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV", Research Notes in Mathematics, 39, pp.136~212 (1979)
  16. J. Serrin, "On the interior regularity of weak solutions of the Navier-Stokes equations", Archive for Rational Mechanics and Analysis, 9, pp.187~195 (1962)
  17. E. M. Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, With the assistance of Timothy S. Murphy. Princeton Mathematical Series, 43. Monographs in Harmonic Analysis, III" (1993), Princeton University Press
  18. E. M. Stein, "Introduction to Fourier Analysis on Euclidean Spaces, Princeton Mathematical Series, No. 32" (1971), Princeton University Press
  19. M. E. Taylor, "Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations", Communications in Partial Differential Equations, 17(9), pp.1407~1456 (1992)
  20. R. Temam, "Navier-Stokes Equations, Studies in Mathematics and its Applications, Vol. 2" (1977), North-Holland Publishing Co.

관련 논문AI추천

New regularity criterion for the Navier-Stokes equationsHu Yue, Yuanshan Zhaoy장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2009 · 제12권 제3호On the improved regularity criterion of the solutions to the Navier-Stokes equationsSadek Gala대한수학회 · 대한수학회논문집2020 · 제35권 제1호NAVIER-STOKES EQUATIONS IN BESOV SPACE B−s ∞,∞(Rn +)진범자대한수학회 · 대한수학회지2013 · 제50권 제4호Local regularity criteria of the Navier-Stokes equations with slip boundary conditions강경근, 김명현, 배형옥대한수학회 · 대한수학회지2016 · 제53권 제3호Navier-Stokes equations with anisotropic regularity in one velocity componentXian Yang, Xiqin Ouyang, Zujin Zhang장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제3호Existence of strong mild solution of the Navier-Stokes equations in the half space with nondecaying initial data배형옥, 진범자대한수학회 · 대한수학회지2012 · 제49권 제1호

이 간행물의 다른 논문 (19건)

Linear preservers of spanning column rank of matrix sums over semirings송석준pp. 301-312Schatten's theorem on absolute Schur algebrasPachara Chaisuriya, Jitti Rakbudpp. 313-329On some new nonlinear retarded integral inequalities with iterated integrals and their applicationsQing-Hua Ma, Josip Pecaricpp. 331-353Complete moment convergence of moving average processes with dependent innovations김태성, 최용갑, 고미화pp. 355-365DIAGONAL LIFTS OF TENSOR FIELDS OF TYPE (1, 1) ON CROSS-SECTIONS IN TENSOR BUNDLES AND ITS APPLICATIONSArif Salimov, Aydin Gezerpp. 367-376
원문 보기