Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (4): 1607-1620.doi: 10.1007/s10473-022-0418-z
• Articles • Previous Articles Next Articles
Yajuan ZHAO1, Yongsheng LI2, Wei YAN3, Xiangqian YAN3
Received:
2020-04-15
Revised:
2021-06-04
Online:
2022-08-25
Published:
2022-08-23
Contact:
Yajuan ZHAO,E-mail:zhaoyj_91@zzu.edu.cn
E-mail:zhaoyj_91@zzu.edu.cn
Supported by:
CLC Number:
Yajuan ZHAO, Yongsheng LI, Wei YAN, Xiangqian YAN. ON THE DIMENSION OF THE DIVERGENCE SET OF THE OSTROVSKY EQUATION[J].Acta mathematica scientia,Series B, 2022, 42(4): 1607-1620.
[1] Adams D R. Anote on the Choquet integrals with respect to Hausdorff capacity. Function spaces and applications[M]. Berline:Springer-Verlag, 1988 [2] Barceló J A, Bennett J, Carbery A, et al, On the dimension of divergence sets of dispersive equations[J]. Math Ann, 2011, 349:599-622 [3] Bourgain J, On the Schrödinger maximal function in higher dimension[J]. Proc Steklov Inst Math, 2013, 280:46-60 [4] Bourgain J, A note on the Schrödinger maximal function[J]. J Anal Math, 2016, 130:393-396 [5] Carleson L. Some analytical problems related to statistical mechanics//Euclidean Harmonic Analysisi[M]. Berlin:Springer, 1979 [6] Coclite G M, di Ruvo L, On the solutions for an Ostrovsky type equation[J]. Nonlinear Anal Real World Appl, 2020, 55:31 pp [7] Dahlberg B E, Kenig C E. Anote on the almost everywhere behavior of solutions to the Schrödinger equation[M]. Berlin:Springer, 1981 [8] Ding Y, Niu Y, Global L2 estimates for a class of maximal operators associated to general dispersive equations[J]. J Inequal Appl, 2015, 199:20 pp [9] Ding Y, Niu Y, Maximal estimate for solutions to a class of dispersive equation with radial initial value[J]. Front Math China, 2017, 12:1057-1084 [10] Du X M, Guth L, Li X C, A sharp Schrödinger maximal estimate in R2[J]. Ann Math, 2017, 188:607-640 [11] Du X M, Zhang R X. Sharp L2 estimates of the Schrödinger maximal function in higher dimensions[J]. Ann Math, 2019, 189:837-861 [12] Galkin V N, Stepanyants Y A, On the existence of stationary solitary waves in a rotating fluid[J]. J Appl Math Mech, 1991, 55:939-943 [13] Gui G L, Liu Y, On the Cauchy problem for the Ostrovsky equation with positive dispersion[J]. Comm Partial Differential Equations, 2007, 32:1895-1916 [14] Huo Z H, Jia Y L, Low-regularity solutions for the Ostrovsky equation[J]. Proc Edinb Math Soc, 2006, 49:87-100 [15] Isaza P, Mejía J, Cauchy problem for the Ostrovsky equation in spaces of low regularity[J]. J Diff Eqns, 2006, 230:661-681 [16] Isaza P, Mejía J, On the support of solutions to the Ostrovsky equation withpositive dispersion[J]. Nonlinear Anal TMA, 2010, 72:4016-4029 [17] Kenig C E, Ponce G, Vega L, Oscillatory integrals and regularity of dispersive equations[J]. India Uni Math J, 1991, 40:33-69 [18] Lee S. On pointwise convergence of the solutions to Schrödinger equations in R2[J]. Int Math Res Not, 2006, Art ID 32597, 21 pp [19] Leonov A, The effect of the earth's rotation on the propagation of weak nonlinear surface and internal long oceanic waves[J]. Ann New York Acad Sci, 1981, 373:150-159 [20] Li D, Li J F, On 4-order Schröodinger operator and Beam operator[J]. Front Math China, 2019, 14:1197-1211 [21] Li D, Li J F, Xiao J. A Carleson problem for the Boussinesq operator[J]. arXiv:1912.09636v1[math.CA] 20 Dec 2019 [22] Linares F, Milanés A, Local and global well-posedness for the Ostrovsky equation[J]. J Diff Eqns, 2006, 222:325-340 [23] Lucà R, Rogers K, A note on pointwise convergence for the Schrödinger equation[J]. Math Proc Cambridge Philos Soc, 2019, 166:209-218 [24] Mattila P. Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability[M]. Cambridge:Cambridge University, 1995 [25] Miao C X, Zhang J Y, Zheng J Q, Maximal estimates for Schrödinger equation with inverse-square potential[J]. Pac J Math, 2015, 273:1-19 [26] Ostrovskii L A, Nonlinear internal waves in a rotating ocean[J]. Okeanologiya, 1978, 18:181-191 [27] Sjögren P, Sjölin P, Convergence properties for the time-dependent Schröodinger equation. Ann Acad Sci Fenn Ser A I Math, 1989, 14:13-25 [28] Sjöolin P, Maximal estimates for solutions to the nonelliptic Schröodinger equation[J]. Bull Lond Math Soc, 2007, 39:404-412 [29] Stein E M. Harmonic Analysis:real-variable methods, orthogonality, and oscillatory integrals[M]. Princeton:Princeton University, 1993 [30] Varlamov V, Liu Y, Cauchy problem for the Ostrovsky equation[J]. Discrete Contin Dyn Syst, 2004, 10:731-753 [31] Vega L, Schrödinger equations:pointwise convergence to the initial data[J]. Proc Amer Math Soc, 1988, 102:874-878 [32] Yan W, Li Y S, Huang J H, et al, The Cauchy problem for the Ostrovsky equation with positive dispersion[J]. NoDEA Nonlinear Differential Equations Appl, 2018, 25:37 pp [33] Yan W, Zhang Q Q, Duan J Q, et al. Pointwise convergence problem of Ostrovsky equation with rough data and random data. arXiv:2006.15981v1[math.AP] 24 Jun 2020 [34] Wang J F, Yan W, The Cauchy problem for quadratic and cubic Ostrovsky equation with negative dispersion[J]. Nonlinear Anal Real World Appl, 2018, 43:283-307 [35] Žubrinić D, Singular sets of Sobolev functions[J]. C R Math Acad Sci Paris, 2002, 334:539-544 |
[1] | Jun WANG, Zhenlong CHEN. HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS [J]. Acta mathematica scientia,Series B, 2022, 42(2): 653-670. |
[2] | Dan LI, Junfeng LI, Jie XIAO. AN UPBOUND OF HAUSDORFF'S DIMENSION OF THE DIVERGENCE SET OF THE FRACTIONAL SCHRÖDINGER OPERATOR ON Hs(Rn) [J]. Acta mathematica scientia,Series B, 2021, 41(4): 1223-1249. |
[3] | Jianfeng ZHOU, Zhong TAN. REGULARITY OF WEAK SOLUTIONS TO A CLASS OF NONLINEAR PROBLEM [J]. Acta mathematica scientia,Series B, 2021, 41(4): 1333-1365. |
[4] | Zhenliang ZHANG, Chunyun CAO. ON POINTS CONTAIN ARITHMETIC PROGRESSIONS IN THEIR LÜROTH EXPANSION [J]. Acta mathematica scientia,Series B, 2016, 36(1): 257-264. |
[5] | CHEN Zhen-Long. ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES [J]. Acta mathematica scientia,Series B, 2014, 34(1): 141-161. |
[6] | HU Dong-Gang, HU Xue-Hai. ARBITRARILY LONG ARITHMETIC PROGRESSIONS FOR CONTINUED FRACTIONS OF LAURENT SERIES [J]. Acta mathematica scientia,Series B, 2013, 33(4): 943-949. |
[7] | CHEN Zhen-Long. FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES [J]. Acta mathematica scientia,Series B, 2011, 31(3): 969-992. |
[8] | CHEN Zhen-Long, LI Hui-Qiong. POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS [J]. Acta mathematica scientia,Series B, 2010, 30(3): 857-872. |
[9] | Chen Zhenlong. INTERSECTIONS AND POLAR FUNCTIONS OF FRACTIONAL BROWNIAN SHEETS [J]. Acta mathematica scientia,Series B, 2008, 28(4): 779-796. |
[10] | Gao Junyang; Qiao Jianyong. CONTINUITY AND HAUSDORFF DIMENSION OF JULIA SET CONCERNING YANG-LEE ZEROS [J]. Acta mathematica scientia,Series B, 2008, 28(3): 530-536. |
[11] | Hu Dihe; Zhang Xiaomin. THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET [J]. Acta mathematica scientia,Series B, 2007, 27(3): 561-573. |
[12] | Hu Dihe; Zhang Xiaomin. THE RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET [J]. Acta mathematica scientia,Series B, 2007, 27(2): 267-273. |
[13] | Zhang Xiaomin; Hu Dihe. THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS [J]. Acta mathematica scientia,Series B, 2006, 26(4): 615-628. |
[14] | ZHANG Xiao-Qun, LIU Pan-Yan. THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS [J]. Acta mathematica scientia,Series B, 2004, 24(3): 485-492. |
[15] |
XU Jing-Hu, DING Li-Xin.
HAUSDORFF DIMENSION OF GENERALIZED STATISTICALLY SELF-AFFINE FRACTALS [J]. Acta mathematica scientia,Series B, 2004, 24(3): 421-433. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||
Full text 4
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Abstract 92
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||
Shared | ||||||||||||||||||||||||||||||||||||||||||||||
Discussed |
|