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Global solutions to 1D compressible Navier-Stokes/Allen-Cahn system with density-dependent viscosity and free-boundary 具有密度依赖粘度和自由边界的一维可压缩Navier-Stokes/Allen-Cahn系统的全局解
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0111-5
Shijin Ding, Yinghua Li, Yu Wang
{"title":"Global solutions to 1D compressible Navier-Stokes/Allen-Cahn system with density-dependent viscosity and free-boundary","authors":"Shijin Ding,&nbsp;Yinghua Li,&nbsp;Yu Wang","doi":"10.1007/s10473-024-0111-5","DOIUrl":"10.1007/s10473-024-0111-5","url":null,"abstract":"<div><p>This paper is concerned with the Navier-Stokes/Allen-Cahn system, which is used to model the dynamics of immiscible two-phase flows. We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form of <i>η</i>(<i>ρ</i>) = <i>ρ</i><sup><i>α</i></sup>. The existence of unique global <i>H</i><sup>2<i>m</i></sup>-solutions (<i>m</i> ∈ ℕ) to the free boundary problem is proven for when <span>(0 &lt; alpha &lt; {1 over 4})</span>. Furthermore, we obtain the global <i>C</i><sup>∞</sup>-solutions if the initial data is smooth.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"195 - 214"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473089","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
Convexity of the free boundary for an axisymmetric incompressible impinging jet 轴对称不可压缩冲击射流自由边界的凹凸性
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0113-3
Xiaohui Wang
{"title":"Convexity of the free boundary for an axisymmetric incompressible impinging jet","authors":"Xiaohui Wang","doi":"10.1007/s10473-024-0113-3","DOIUrl":"10.1007/s10473-024-0113-3","url":null,"abstract":"<div><p>This paper is devoted to the study of the shape of the free boundary for a three-dimensional axisymmetric incompressible impinging jet. To be more precise, we will show that the free boundary is convex to the fluid, provided that the uneven ground is concave to the fluid.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"234 - 246"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473139","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 interior transmission eigenvalue problem for an anisotropic medium by a partially coated boundary 具有部分包覆边界的各向异性介质的内部传输特征值问题
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0118-y
Jianli Xiang, Guozheng Yan
{"title":"The interior transmission eigenvalue problem for an anisotropic medium by a partially coated boundary","authors":"Jianli Xiang,&nbsp;Guozheng Yan","doi":"10.1007/s10473-024-0118-y","DOIUrl":"10.1007/s10473-024-0118-y","url":null,"abstract":"<div><p>We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary ∂Ω is split into two disjoint parts and possesses different transmission conditions. Using the variational method, we obtain the well posedness of the interior transmission problem, which plays an important role in the proof of the discreteness of eigenvalues. Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that <i>n</i> ≡ 1, where a fourth order differential operator is applied. In the case of <i>n</i> ≢ 1, we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"339 - 354"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473076","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
Some properties of the integration operators on the spaces F(p, q, s) 空间F(p, q, s)上积分算子的一些性质
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0109-z
Jiale Chen
{"title":"Some properties of the integration operators on the spaces F(p, q, s)","authors":"Jiale Chen","doi":"10.1007/s10473-024-0109-z","DOIUrl":"10.1007/s10473-024-0109-z","url":null,"abstract":"<div><p>We study the closed range property and the strict singularity of integration operators acting on the spaces <i>F</i>(<i>p, pα</i> − 2, <i>s</i>). We completely characterize the closed range property of the Volterra companion operator <i>I</i><sub><i>g</i></sub> on <i>F</i>(<i>p, pα</i> − 2, <i>s</i>), which generalizes the existing results and answers a question raised in [A. Anderson, Integral Equations Operator Theory, 69 (2011), no. 1, 87–99]. For the Volterra operator <i>J</i><sub><i>g</i></sub>, we show that, for 0 &lt; <i>α</i> ≤ 1, <i>J</i><sub><i>g</i></sub> never has a closed range on <i>F</i> (<i>p, pα</i> − 2, <i>s</i>). We then prove that the notions of compactness, weak compactness and strict singularity coincide in the case of <i>J</i><sub><i>g</i></sub> acting on <i>F</i>(<i>p,p</i> − 2, <i>s</i>).</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"173 - 188"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473090","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
Nadaraya-Watson estimators for reflected stochastic processes 反射随机过程的Nadaraya-Watson估计量
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0107-1
Yuecai Han, Dingwen Zhang
{"title":"Nadaraya-Watson estimators for reflected stochastic processes","authors":"Yuecai Han,&nbsp;Dingwen Zhang","doi":"10.1007/s10473-024-0107-1","DOIUrl":"10.1007/s10473-024-0107-1","url":null,"abstract":"<div><p>We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations. The estimates, based on either the continuously observed process or the discretely observed process, are considered. Under certain conditions, we prove the strong consistency and the asymptotic normality of the two estimators. Our method is also suitable for one-sided reflected stochastic differential equations. Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis <i>et al.</i> (Stat Sin, 2021, 31: 29–51). Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"143 - 160"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473257","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: 1
Global classical solutions of semilinear wave equations on ({mathbb{R}^3} times mathbb{T}) with cubic nonlinearities ({mathbb{R}^3} times mathbb{T})上具有三次非线性的半线性波动方程的全局经典解
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0105-3
Fei Tao
{"title":"Global classical solutions of semilinear wave equations on ({mathbb{R}^3} times mathbb{T}) with cubic nonlinearities","authors":"Fei Tao","doi":"10.1007/s10473-024-0105-3","DOIUrl":"10.1007/s10473-024-0105-3","url":null,"abstract":"<div><p>In this paper, we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space <span>({mathbb{R}^3} times mathbb{T})</span>. The semilinear nonlinearity is assumed to be of the cubic form. The main ingredient here is the establishment of the <i>L</i><sup>2</sup>–<i>L</i><sup>∞</sup> decay estimates and the energy estimates for the linear problem, which are adapted to the wave equation on the product space. The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction, the scaling technique, and the combination of the decay estimates and the energy estimates.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"115 - 128"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473280","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
Complete Kähler metrics with positive holomorphic sectional curvatures on certain line bundles (related to a cohomogeneity one point of view on a Yau conjecture) 在某些线束上具有正全纯截面曲率的完备Kähler度量(与丘猜想上的同质性一点有关)
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0103-5
Xiaoman Duan, Zhuangdan Guan
{"title":"Complete Kähler metrics with positive holomorphic sectional curvatures on certain line bundles (related to a cohomogeneity one point of view on a Yau conjecture)","authors":"Xiaoman Duan,&nbsp;Zhuangdan Guan","doi":"10.1007/s10473-024-0103-5","DOIUrl":"10.1007/s10473-024-0103-5","url":null,"abstract":"<div><p>In this article, we study Kähler metrics on a certain line bundle over some compact Kähler manifolds to find complete Kähler metrics with positive holomorphic sectional (or bisectional) curvatures. Thus, we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"78 - 102"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473320","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: 2
A class of inverse quotient curvature flow in the AdS-Schwarzschild manifold AdS-Schwarzschild流形中的一类逆商曲率流
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0614-5
Zhengchao Ji
{"title":"A class of inverse quotient curvature flow in the AdS-Schwarzschild manifold","authors":"Zhengchao Ji","doi":"10.1007/s10473-023-0614-5","DOIUrl":"10.1007/s10473-023-0614-5","url":null,"abstract":"<div><p>In this paper, we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold. We prove that under suitable convex conditions for the initial hypersurface, one can get the long-time existence for the inverse curvature flow. Moreover, we also get that the principal curvatures of the evolving hypersurface converge to 1 when <i>t</i> → +∞.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2553 - 2572"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908933","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
Characteizations of woven g-frames and weaving g-frames in Hilbert spaces and C*-modules Hilbert空间和C*-模中的编织g-框架和编织g-帧的性质
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0609-2
Amir Khosravi, Mohammad Reza Farmani
{"title":"Characteizations of woven g-frames and weaving g-frames in Hilbert spaces and C*-modules","authors":"Amir Khosravi,&nbsp;Mohammad Reza Farmani","doi":"10.1007/s10473-023-0609-2","DOIUrl":"10.1007/s10473-023-0609-2","url":null,"abstract":"<div><p>In this paper, using Parseval frames we generalize Sun’s results to g-frames in Hilbert <i>C</i>*-modules. Moreover, for g-frames in Hilbert spaces, we present some characterizations in terms of a family of frames, not only for orthonormal bases. Also, we have a note about a comment and a relation in the proof of Proposition 5.3 in [D. Li et al., On weaving g-frames for Hilbert spaces, Complex Analysis and Operator Theory, 2020]. Finally, we have some results for g-Riesz bases, woven and P-woven g-frames.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2471 - 2482"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908927","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
Transportation cost-information inequality for a stochastic heat equation driven by fractional-colored noise 分数有色噪声驱动的随机热方程的运输成本信息不等式
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0612-7
Ruinan Li, Xinyu Wang
{"title":"Transportation cost-information inequality for a stochastic heat equation driven by fractional-colored noise","authors":"Ruinan Li,&nbsp;Xinyu Wang","doi":"10.1007/s10473-023-0612-7","DOIUrl":"10.1007/s10473-023-0612-7","url":null,"abstract":"<div><p>In this paper, we prove Talagrand’s <b>T</b><sub><b>2</b></sub> transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise, which is fractional for a time variable with the Hurst index <span>(H in ({1 over 2},1))</span>, and is correlated for the spatial variable. The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2519 - 2532"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908935","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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