This note deals with the question of the regularity of (Leray) weak solutions of the Navier-Stokes equations in terms of the pressure. This criterion improves on the existing results.
{"title":"ON THE IMPROVED REGULARITY CRITERION OF THE SOLUTIONS TO THE NAVIER-STOKES EQUATIONS","authors":"S. Gala","doi":"10.4134/CKMS.C190019","DOIUrl":"https://doi.org/10.4134/CKMS.C190019","url":null,"abstract":"This note deals with the question of the regularity of (Leray) weak solutions of the Navier-Stokes equations in terms of the pressure. This criterion improves on the existing results.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70436566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ON A NEW CLASS OF FUNCTIONS RELATED WITH MITTAG-LEFFLER AND WRIGHT FUNCTIONS AND THEIR PROPERTIES","authors":"D. Bansal, K. Mehrez","doi":"10.4134/CKMS.C200022","DOIUrl":"https://doi.org/10.4134/CKMS.C200022","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70437978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, our main objective is to introduce the notion of conformal hemi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalized case of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. We mainly focus on conformal hemi-slant submersions from K¨ahler manifolds. During this manner, we tend to study and investigate integrability of the distributions which are arisen from the definition of the submersions and the geometry of leaves of such distributions. Moreover, we tend to get necessary and sufficient conditions for these submersions to be totally geodesic for such manifolds. We also provide some quality examples of conformal hemi-slant submersions.
{"title":"CONFORMAL HEMI-SLANT SUBMERSIONS FROM ALMOST HERMITIAN MANIFOLDS","authors":"Sumeet Kumar, Sushil Kumar, S. Pandey, R. Prasad","doi":"10.4134/CKMS.C190448","DOIUrl":"https://doi.org/10.4134/CKMS.C190448","url":null,"abstract":". In this paper, our main objective is to introduce the notion of conformal hemi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalized case of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. We mainly focus on conformal hemi-slant submersions from K¨ahler manifolds. During this manner, we tend to study and investigate integrability of the distributions which are arisen from the definition of the submersions and the geometry of leaves of such distributions. Moreover, we tend to get necessary and sufficient conditions for these submersions to be totally geodesic for such manifolds. We also provide some quality examples of conformal hemi-slant submersions.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"RELATION BETWEEN KNEADING MATRICES OF A MAP AND ITS ITERATES","authors":"C. Gopalakrishna, Murugan Veerapazham","doi":"10.4134/CKMS.C190255","DOIUrl":"https://doi.org/10.4134/CKMS.C190255","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70437481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"PROPERTIES OF k th -ORDER (SLANT TOEPLITZ + SLANT HANKEL) OPERATORS ON H 2 ()","authors":"Anuradha Gupta, B. Gupta","doi":"10.4134/CKMS.C190403","DOIUrl":"https://doi.org/10.4134/CKMS.C190403","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70437965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"TOPOLOGICAL STABILITY IN HYPERSPACE DYNAMICAL SYSTEMS","authors":"Namjip Koo, Hyunhee Lee, Nyamdavaa Tsegmid","doi":"10.4134/CKMS.C200058","DOIUrl":"https://doi.org/10.4134/CKMS.C200058","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source ut−4u− 4ut = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ Rn (n ≥ 1). Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.
{"title":"BLOW-UP TIME AND BLOW-UP RATE FOR PSEUDO-PARABOLIC EQUATIONS WITH WEIGHTED SOURCE","authors":"Huafei Di, Y. Shang","doi":"10.4134/CKMS.C200035","DOIUrl":"https://doi.org/10.4134/CKMS.C200035","url":null,"abstract":"In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source ut−4u− 4ut = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ Rn (n ≥ 1). Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jin [7] defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an (`, m)-type connection. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (`,m)type connection in [7]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an (`,m)-type connection.
{"title":"GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH A NON-SYMMETRIC NON-METRIC CONNECTION OF TYPE (ℓ, m)","authors":"Chul Woo Lee, Jae Won Lee","doi":"10.4134/CKMS.C200055","DOIUrl":"https://doi.org/10.4134/CKMS.C200055","url":null,"abstract":"Jin [7] defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an (`, m)-type connection. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (`,m)type connection in [7]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an (`,m)-type connection.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70438544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"BIHARMONIC CURVES IN 3-DIMENSIONAL LORENTZIAN SASAKIAN SPACE FORMS","authors":"J. Lee","doi":"10.4134/CKMS.C190393","DOIUrl":"https://doi.org/10.4134/CKMS.C190393","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70437854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"MODULE DERIVATIONS ON COMMUTATIVE BANACH MODULES","authors":"M. Amini, A. Bodaghi, B. Shojaee","doi":"10.4134/CKMS.C200020","DOIUrl":"https://doi.org/10.4134/CKMS.C200020","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70437913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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