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Evolution and interaction of δ-waves in the zero-pressure gas dynamics system 零压气体动力学系统中δ波的演变和相互作用
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0510-7
Abhishek Das, K. T. Joseph
{"title":"Evolution and interaction of δ-waves in the zero-pressure gas dynamics system","authors":"Abhishek Das, K. T. Joseph","doi":"10.1007/s10473-024-0510-7","DOIUrl":"https://doi.org/10.1007/s10473-024-0510-7","url":null,"abstract":"<p>Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system. In this paper, we study the initial value problem for one dimensional zero-pressure gas dynamics system. Here the first equation is the Burgers equation and the second one is the continuity equation. We consider the solution with initial data in the space of bounded Borel measures. First we prove a general existence result in the algebra of generalized functions of Colombeau. Then we study in detail special solutions with <i>δ</i>-measures as initial data. We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves. This gives an understanding of plane-wave interactions in the multidimensional case. We use the vanishing viscosity method in our analysis as this gives the physical solution.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"23 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime 流体-粒子相互作用模型流态平稳解的全局存在性和唯一性
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0513-4
Lin Zheng, Shu Wang
{"title":"The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime","authors":"Lin Zheng, Shu Wang","doi":"10.1007/s10473-024-0513-4","DOIUrl":"https://doi.org/10.1007/s10473-024-0513-4","url":null,"abstract":"<p>This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in ℝ<sup>3</sup>. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence and uniqueness of global smooth solutions in <i>H</i><sup>3</sup> of the system are established by using the careful energy method.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"37 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Toeplitz determinants in one and higher dimensions 一维及更高维度的托普利兹行列式
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0517-0
Surya Giri, S. Sivaprasad Kumar
{"title":"Toeplitz determinants in one and higher dimensions","authors":"Surya Giri, S. Sivaprasad Kumar","doi":"10.1007/s10473-024-0517-0","DOIUrl":"https://doi.org/10.1007/s10473-024-0517-0","url":null,"abstract":"<p>In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk <span>(mathbb{U})</span>. Furthermore, these results are extended to a class of holomorphic functions on the unit ball in a complex Banach space and on the unit polydisc in ℂ<sup><i>n</i></sup>. The obtained results provide the bounds of Toeplitz determinants in higher dimensions for various subclasses of normalized univalent functions.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"23 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global unique solutions for the incompressible MHD equations with variable density and electrical conductivity 密度和导电率可变的不可压缩多流体力学方程的全局唯一解
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0507-2
Xueli Ke
{"title":"Global unique solutions for the incompressible MHD equations with variable density and electrical conductivity","authors":"Xueli Ke","doi":"10.1007/s10473-024-0507-2","DOIUrl":"https://doi.org/10.1007/s10473-024-0507-2","url":null,"abstract":"<p>We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data (<i>u</i><sub>0</sub>, <i>B</i><sub>0</sub>) being located in the critical Besov space <span>(dot{B}_{p,1}^{{-1}+{{2}over{p}}}(mathbb{R}^{2}))</span> (1 &lt; <i>p</i> &lt; 2) and the initial density <i>ρ</i><sub>0</sub> being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normalized solutions for the general Kirchhoff type equations 一般基尔霍夫方程的归一化解法
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0514-3
Wenmin Liu, Xuexiu Zhong, Jinfang Zhou
{"title":"Normalized solutions for the general Kirchhoff type equations","authors":"Wenmin Liu, Xuexiu Zhong, Jinfang Zhou","doi":"10.1007/s10473-024-0514-3","DOIUrl":"https://doi.org/10.1007/s10473-024-0514-3","url":null,"abstract":"<p>In the present paper, we prove the existence, non-existence and multiplicity of positive normalized solutions (<i>λ</i><sub><i>c</i></sub>, <i>u</i><sub><i>c</i></sub>) ∈ ℝ × <i>H</i><sup>1</sup> (ℝ<sup><i>N</i></sup>) to the general Kirchhoff problem</p><span>$$-Mleft(int_{mathbb{R}^N}vertnabla uvert^2 {rm d}xright)Delta u +lambda u=g(u)~hbox{in}~mathbb{R}^N, uin H^1(mathbb{R}^N),Ngeq 1,$$</span><p>satisfying the normalization constraint <span>(int_{mathbb{R}^N}u^2{rm d}x=c)</span>, where <i>M</i> ∈ <i>C</i>([0, ∞)) is a given function satisfying some suitable assumptions. Our argument is not by the classical variational method, but by a global branch approach developed by Jeanjean <i>et al.</i> [J Math Pures Appl, 2024, 183: 44–75] and a direct correspondence, so we can handle in a unified way the nonlinearities <i>g</i>(<i>s</i>), which are either mass subcritical, mass critical or mass supercritical.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"109 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Big Hankel operators on Hardy spaces of strongly pseudoconvex domains 强伪凸域哈代空间上的大汉克尔算子
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-05-01 DOI: 10.1007/s10473-024-0301-1
{"title":"Big Hankel operators on Hardy spaces of strongly pseudoconvex domains","authors":"","doi":"10.1007/s10473-024-0301-1","DOIUrl":"https://doi.org/10.1007/s10473-024-0301-1","url":null,"abstract":"<h3>Abstract</h3> <p>In this article, we investigate the (big) Hankel operator <em>H</em><sub><em>f</em></sub> on the Hardy spaces of bounded strongly pseudoconvex domains Ω in ℂ<sup><em>n</em></sup>. We observe that <em>H</em><sub><em>f</em></sub> is bounded on <em>H</em><sup><em>p</em></sup> (Ω) (1 &lt; p &lt; ∞) if <em>f</em> belongs to BMO and we obtain some characterizations for <em>H</em><sub><em>f</em></sub> on <em>H</em><sup>2</sup> (Ω) of other pseudoconvex domains. In these arguments, Amar’s <em>L</em><sup><em>p</em></sup>-estimations and Berndtsson’s <em>L</em><sup>2</sup>-estimations for solutions of the <span> <span>({{bar partial }_b})</span> </span>-equation play a crucial role. In addition, we solve Gleason’s problem for Hardy spaces <em>H</em><sup><em>p</em></sup>(Ω) (1 ≤ p ≤ ∞) of bounded strongly pseudoconvex domains.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"128 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The global existence of strong solutions for a non-isothermal ideal gas system 非等温理想气体系统强解的全局存在性
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-05-01 DOI: 10.1007/s10473-024-0306-9
{"title":"The global existence of strong solutions for a non-isothermal ideal gas system","authors":"","doi":"10.1007/s10473-024-0306-9","DOIUrl":"https://doi.org/10.1007/s10473-024-0306-9","url":null,"abstract":"<h3>Abstract</h3> <p>We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space <strong><em>H</em></strong><sup>2</sup> (ℝ<sup>3</sup>) for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space <span> <span>(dot{boldsymbol{B}}_{boldsymbol{2,1}}^{boldsymbol{3/2}})</span> </span> by showing that the linearized operator is a contraction mapping under the right circumstances.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B p n of ℂn ℂn的莱因哈特域B p n上的边界施瓦茨定理和刚性定理
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-05-01 DOI: 10.1007/s10473-024-0304-y
{"title":"The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B p n of ℂn","authors":"","doi":"10.1007/s10473-024-0304-y","DOIUrl":"https://doi.org/10.1007/s10473-024-0304-y","url":null,"abstract":"<h3>Abstract</h3> <p>By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit <em>p</em>-ball <em>B</em><span> <sub><em>p</em></sub> <sup><em>n</em></sup> </span> of ℂ<sup><em>n</em></sup>. Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on <em>B</em><span> <sub><em>p</em></sub> <sup><em>n</em></sup> </span> is obtained. These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for <em>p</em> = 2, and the unit polydisk for <em>p</em> = ∞, respectively.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"76 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Starlikeness associated with the sine hyperbolic function 与正弦双曲线函数相关的星光性
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-04-16 DOI: 10.1007/s10473-024-0404-8
Mohsan Raza, Hadiqa Zahid, Jinlin Liu
{"title":"Starlikeness associated with the sine hyperbolic function","authors":"Mohsan Raza, Hadiqa Zahid, Jinlin Liu","doi":"10.1007/s10473-024-0404-8","DOIUrl":"https://doi.org/10.1007/s10473-024-0404-8","url":null,"abstract":"<p>Let <i>qλ</i> (<i>z</i>) = 1 + <i>λ</i>sinh(<i>ς</i>), 0 &lt; <i>λ</i> &lt; 1/sinh(1) be a non-vanishing analytic function in the open unit disk. We introduce a subclass <span>({{cal S}^ * }({q_lambda }))</span> (<i>qλ</i>) of starlike functions which contains the functions <span>(mathfrak{f})</span> such that <span>(z{mathfrak{f}^prime }/mathfrak{f})</span> is subordinated by <i>qλ</i>. We establish inclusion and radii results for the class <span>({{cal S}^ * })</span> (<i>qλ</i>) for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class <span>({{cal S}^ * })</span> (<i>qλ</i>). We also find a sharp bound for the third Hankel determinant for the case <i>λ</i> = 1/2.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"20 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140617646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Blow-up conditions for a semilinear parabolic system on locally finite graphs 局部有限图上半线性抛物系统的炸毁条件
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-03-01 DOI: 10.1007/s10473-024-0213-0
{"title":"Blow-up conditions for a semilinear parabolic system on locally finite graphs","authors":"","doi":"10.1007/s10473-024-0213-0","DOIUrl":"https://doi.org/10.1007/s10473-024-0213-0","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition <em>CDE’</em>(<em>n</em>,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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