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Logarithmically improved regularity criteria for the Navier-Stokes equations in homogeneous Besov spaces

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dc.contributor.authorDíaz Díaz, Jesús Ildefonso
dc.date.accessioned2023-06-17T08:32:27Z
dc.date.available2023-06-17T08:32:27Z
dc.date.issued2021
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/77489
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7398
dc.journal.titleElectronic Journal of Differential Equations
dc.language.isoeng
dc.page.final9
dc.page.initial1
dc.publisherTexas State University, Department of Mathematics
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/es/
dc.subject.cdu517
dc.subject.keywordBesov space
dc.subject.keywordNavier-Stokes equations
dc.subject.keywordRegularity criteria
dc.subject.ucmAnálisis matemático
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleLogarithmically improved regularity criteria for the Navier-Stokes equations in homogeneous Besov spaces
dc.typejournal article
dc.volume.number89
dcterms.references[1] J. T. Beale, T. Kato, A. Majda; Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Commun. Math. Phys., 94 (1984), 61–66. [2] H. Beirao da Veiga; A new regularity class for the Navier-Stokes equations in Rn, Chin. Ann. Math., 16 (1995), 407–412. [3] N. A. Dao, J. I. D´ıaz, Q. H. Nguyen; Generalized Gagliardo-Nirenberg inequalities using Lorentz spaces andz BMO, Nonlinear Analysis: Theory, Methods, Applications, 173 (2018), 146–153. 4] L. Ecauriaza, G. A. Seregin, V. Sverák; L3,∞-solutions of the Navier-Stokes equations and backward uniqueness, Russ. Math. Surv., 58 (2003), 211–248. [5] J. Fan, S. Jiang, G. Nakamura; On logarithmically improved regularity criteria for the NavierStokes equations in Rn, IMA Journal of Applied Mathematics, 76 (2011), 298–311. [6] J. Fan, S. Jiang, G. Nakamura, Y. Zhou; Logarithmically improved regularity criteria for the Navier-Stokes and MHD equations, J. Math. Fluid Mech., 13 (2011), 557-571. [7] Y. Giga; Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system, J. Diff. Equ., 62 (1986), 186–212. [8] E. Hopf; Uber die Anfangswertaufabe f¨ur die hydrodynamischen Grundgleichungen, Math. Nachr., 4 (1951), 213–23l. [9] B. Jawerth; Some observations on Besov and Lizorkin-Triebel spaces, Math. Scand., 40 (1977), 94–104. [10] T. Kato, Strong; Lp-solutions of the Navier-Stokes equation in Rm, with applications to weak solutions, Math. Z., 187 (1984), 471–480. [11] T. Kato, G. Ponce; Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math., 41 (1988), 891–907. [12] H. Kozono, T. Ogawa, Y. Taniuchi; The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations, Math. Z., 242 (2002), 251–278. [13] H. Kozono, Y. Shimada; Bilinear estimates in homogeneous Triebel–Lizorkin spaces and the Navier-Stokes equations, Math. Nachr., 276 (2004), 63–74. [14] H. Kozono, Y. Taniuchi; Bilinear estimates in BMO and the Navier-Stokes equations, Math. Z., 235 (2000), 173–194. [15] H. Kozono, Y. Taniuchi; Limitting case of the Sobolev inequality in BMO with application to the Euler equations, Comm. Math. Phys., 214 (2000), 191–200. [16] P.G. Lemarié-Rieusset; Recent Developments in the Navier-Stokes Problem, Chapman and Hall/CRC, Boca Raton, 2002. [17] J. Leray; Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math. 63 (1934), 193-248. [18] S. Montgomery-Smith; Conditions implying regularity of the three dimensional Navier-Stokes equation, Appl. Math. 50 (2005), 451–464. [19] K. Nakao, Y. Taniuchi; An alternative proof of logarithmically improved Beale-Kato-Majda type extension criteria for smooth solutions to the Navier-Stokes equations, Nonl. Anal., 176 (2018), 48–55. [20] J. Necas, M. Ruzicka, V. Sverák; On Leray’s self-similar solutions of the Navier-Stokes equations, Acta Math., 176 (1996), 283–294. [21] T. Ohyama; Interior regularity of weak solutions to the Navier-Stokes equation. Proceedings of the Japan Academy, 36 (1960), 273–277. [22] G. Prodi; Un teorema di unicit`a per le equazioni di Navier-Stokes, Ann. Mat. Pura Appl., 48 (1959), 173–182. [23] J. Serrin; On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 9 (1962), 187–195. [24] H. Triebel; Theory of function spaces II. Birkhäuser, 1992
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relation.isAuthorOfPublication.latestForDiscovery34ef57af-1f9d-4cf3-85a8-6a4171b23557

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