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Russian Journal of Mathematical Physics最新文献

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On the Global Existence for a Class of Compressible Non-Newtonian Fluids with Inhomogeneous Boundary Data 论一类边界数据不均匀的可压缩非牛顿流体的全局存在性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020109
J. Muhammad
{"title":"On the Global Existence for a Class of Compressible Non-Newtonian Fluids with Inhomogeneous Boundary Data","authors":"J. Muhammad","doi":"10.1134/S1061920824020109","DOIUrl":"10.1134/S1061920824020109","url":null,"abstract":"<p> This paper is concerned to the study of global existence of weak solutions to a class of compressible non-Newtonian fluids in three-dimensional bounded domain. More precisely, we consider an isentropic compressible non-Newtonian fluid with adiabatic constant <span>(gamma&gt;frac{3}{2})</span>. We study the global existence of an initial boundary value problem with nonhomogeneous Dirichlet boundary conditions by constructing an approximation scheme, energy estimates, and a weak convergence method. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"276 - 298"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solitary Wave Interactions in the Cubic Whitham Equation 立方惠森方程中的孤波相互作用
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020055
M.V. Flamarion, E. Pelinovsky
{"title":"Solitary Wave Interactions in the Cubic Whitham Equation","authors":"M.V. Flamarion,&nbsp;E. Pelinovsky","doi":"10.1134/S1061920824020055","DOIUrl":"10.1134/S1061920824020055","url":null,"abstract":"<p> The vortical Whitham equation is modeled with quadratic and cubic nonlinearity, satisfying the unidirectional dispersion relation used to describe the propagation of nonlinear waves in the presence of a vertically sheared current of constant vorticity. In this article, we neglect the quadratic nonlinearity to numerically investigate solitary wave interactions. We show that the geometric Lax categorization is satisfied; however, an algebraic categorization based on the ratio of the initial solitary wave amplitudes is not possible. Specifically, our numerical simulations indicate that for solitary waves with large amplitudes, the interactions maintain two well-separated crests. Additionally, for solitary waves of different polarities, we find that wave-breaking may occur. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"199 - 208"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Double-Deck Structure in a Fluid Flow Induced by a Uniformly Rotating Disk with Small Irregularities: the Nonsymmetric Case 具有小不规则的匀速转动圆盘诱导的流体流动中的双层结构：非对称情况
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020067
R.K. Gaydukov
{"title":"Double-Deck Structure in a Fluid Flow Induced by a Uniformly Rotating Disk with Small Irregularities: the Nonsymmetric Case","authors":"R.K. Gaydukov","doi":"10.1134/S1061920824020067","DOIUrl":"10.1134/S1061920824020067","url":null,"abstract":"<p> The problem of a uniformly rotating disk with slightly perturbed surface immersed in a viscous fluid is considered for large Reynolds numbers. The asymptotic solutions with double-deck structure of the boundary layer are constructed for a nonsymmetric irregularity localized on the disk surface. The results of numerical simulation of the flow near the surface are presented. The differences between the problem under consideration and the case of an irregularity symmetric with respect to the disk axis of rotation are shown. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"209 - 217"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Generalized Zhang’s Operator and Kastler–Kalau–Walze Type Theorems 广义张氏算子和 Kastler-Kalau-Walze 型定理
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020080
H. Li, Y. Wang, Y. Yang
{"title":"The Generalized Zhang’s Operator and Kastler–Kalau–Walze Type Theorems","authors":"H. Li,&nbsp;Y. Wang,&nbsp;Y. Yang","doi":"10.1134/S1061920824020080","DOIUrl":"10.1134/S1061920824020080","url":null,"abstract":"<p> In this paper, we obtain two Lichnerowicz type formulas for the generalized Zhang’s operator. And we give the proof of the Kastler–Kalau–Walze type theorem for the generalized Zhang’s operator on 4-dimensional oriented compact manifolds with (respectively, without) boundary. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"227 - 254"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform Spectral Asymptotics for a Schrödinger Operator on a Segment with Delta-Interaction 具有三角交互作用的段上薛定谔算子的均匀谱渐近线
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020018
D.I. Borisov, D.M. Polyakov
{"title":"Uniform Spectral Asymptotics for a Schrödinger Operator on a Segment with Delta-Interaction","authors":"D.I. Borisov,&nbsp;D.M. Polyakov","doi":"10.1134/S1061920824020018","DOIUrl":"10.1134/S1061920824020018","url":null,"abstract":"<p> We consider a Schrödinger operator on the segment <span>((0,1))</span> subject to the Dirichlet condition and perturb it by a delta-potential concentrated at the point <span>(x= varepsilon )</span>, where <span>( varepsilon )</span> is a small positive parameter. We show that the perturbed operator converges to the unperturbed one in the norm resolvent sense and this also implies the convergence of the spectrum. However, the latter convergence is true only inside each compact set on the complex plane and it does not characterize the behavior of the total ensemble of the eigenvalues under the perturbation. Our main result is the spectral asymptotics for the eigenvalues of the perturbed operator with an estimate for the error term uniform in the small parameter. This asymptotics involves an additional nonstandard term, which allows us to describe a global behavior of the total ensemble of the eigenvalues under the perturbation. </p><p> <b> DOI</b> 10.1134/S1061920824020018 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"149 - 161"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Semiclassical Asymptotics on Stratified Manifolds 分层流形上的半经典渐近论
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020110
V.E. Nazaikinskii
{"title":"Semiclassical Asymptotics on Stratified Manifolds","authors":"V.E. Nazaikinskii","doi":"10.1134/S1061920824020110","DOIUrl":"10.1134/S1061920824020110","url":null,"abstract":"<p> We study the problem on semiclassical asymptotics for (pseudo)differential equations with singularities on a stratified manifold of a special form—the orbit space <span>(X)</span> of a smooth action of a compact Lie group <span>(G)</span> on a smooth manifold <span>(M)</span>. The operators under consideration are obtained as the restriction of <span>(G)</span>-invariant operators with smooth coefficients on <span>(M)</span> to the subspace of <span>(G)</span>-invariant functions, naturally identified with functions on <span>(X)</span>, and have singularities on strata of positive codimension. The asymptotics are associated with Lagrangian manifolds in the phase space defined by the Marsden–Weinstein symplectic reduction of the cotangent bundle <span>(T^*M)</span> under the action of the group <span>(G)</span>; rapidly oscillating integrals defining the Maslov canonical operator on such manifolds contain exponentials as well as special functions related to representations of the group <span>(G)</span>. For the simplest stratified manifold—a manifold with boundary obtained as the orbit space of a semi-free action of the group <span>( mathbb{S} ^1)</span> on a closed manifold—the corresponding construction of semiclassical asymptotics was realized earlier. Note that, in this case, the class of equations under consideration on manifolds with boundary includes the linearized shallow water equations in a basin with a sloping beach. The present paper deals with the general case. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"299 - 307"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Upslope Propagation of an Adiabatic Normal Mode in a Wedge-Shaped Sea 论绝热正态模式在楔形海中的上坡传播
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020122
V.A. Sergeev
{"title":"On the Upslope Propagation of an Adiabatic Normal Mode in a Wedge-Shaped Sea","authors":"V.A. Sergeev","doi":"10.1134/S1061920824020122","DOIUrl":"10.1134/S1061920824020122","url":null,"abstract":"<p> We study a two-dimensional problem that models sound propagation in a narrow water wedge near a seashore. For the Helmholtz equation, an adiabatic normal mode propagating shoreward along the water wedge is discussed. We describe the phenomena arising when the mode reaches the <i>critical depth</i> and afterwards. Prior to this, the acoustic field is localized in the water wedge. When the critical depth is reached, the energy of the field radiates into the sea bottom. Thereafter, a surface wave propagates inside the bottom along the water-bottom interface, occasionally leaking back into the water wedge. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"308 - 314"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Representation Formula for the Bernoulli Numbers 伯努利数的新表示公式
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S106192082402016X
A. Petojević, H.M. Srivastava, D. Rastovac
{"title":"A New Representation Formula for the Bernoulli Numbers","authors":"A. Petojević,&nbsp;H.M. Srivastava,&nbsp;D. Rastovac","doi":"10.1134/S106192082402016X","DOIUrl":"10.1134/S106192082402016X","url":null,"abstract":"<p> In this paper, we present a presumably new representation of the Bernoulli numbers. We also give an elementary proof of the Akiyama-Tanigawa algorithm for calculating the Bernoulli numbers. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"335 - 338"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Automatic Continuity of every Locally Bunded Homomorphism of a Perfect Connected Lie Group to a Connected Lie Group 完全连通李群到连通李群的每个局部束同构的自动连续性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020134
A.I. Shtern
{"title":"Automatic Continuity of every Locally Bunded Homomorphism of a Perfect Connected Lie Group to a Connected Lie Group","authors":"A.I. Shtern","doi":"10.1134/S1061920824020134","DOIUrl":"10.1134/S1061920824020134","url":null,"abstract":"<p> One of the simplest and most important results following directly from the commutativity of the discontinuity group of a locally bounded homomorphism between connected Lie groups is the automatic continuity of every locally bounded homomorphism of a perfect Lie group which is proved here. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"315 - 316"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","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 (delta)-Suns and (gamma)-Suns in Asymmetric Spaces 非对称空间中 $$delta$$ -Suns 和 $$gamma$$ -Suns 的凸性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020158
I.G. Tsar’kov
{"title":"Convexity of (delta)-Suns and (gamma)-Suns in Asymmetric Spaces","authors":"I.G. Tsar’kov","doi":"10.1134/S1061920824020158","DOIUrl":"10.1134/S1061920824020158","url":null,"abstract":"<p> Convexity of <span>(delta)</span>-suns and <span>(gamma)</span>-suns is studied in asymmetric spaces with due consideration of geometric properties of the spaces. Known results for usual normed spaces are carried over to the case of general asymmetric normed spaces. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"325 - 334"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","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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