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Erratum to: “Solitary Wave Interactions in the Cubic Whitham Equation” [RJMP 31 (2), 199–208 (2024)] 勘误："立方惠森方程中的孤波相互作用》[RJMP 31 (2)，199-208 (2024)] 更正
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030208
M.V. Flamarion, E. Pelinovsky
{"title":"Erratum to: “Solitary Wave Interactions in the Cubic Whitham Equation” [RJMP 31 (2), 199–208 (2024)]","authors":"M.V. Flamarion, E. Pelinovsky","doi":"10.1134/S1061920824030208","DOIUrl":"10.1134/S1061920824030208","url":null,"abstract":"","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"575 - 575"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409645","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
Remarks on the Uniqueness of Weak Solutions of the Incompressible Navier–Stokes Equations 关于不可压缩纳维-斯托克斯方程弱解唯一性的评论
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030154
K.N. Soltanov
{"title":"Remarks on the Uniqueness of Weak Solutions of the Incompressible Navier–Stokes Equations","authors":"K.N. Soltanov","doi":"10.1134/S1061920824030154","DOIUrl":"10.1134/S1061920824030154","url":null,"abstract":"<p> This paper studies the uniqueness of a weak solution of the incompressible Navier–Stokes Equations in the 3-dimensional case. Here the investigation is provided by using two different approaches. The first (the main) result is obtained for given functions possessing a certain smoothness, using a new approach. The other result works without additional conditions but is, in some sense, a “local” result, investigated by another approach. In addition, here the solvability and uniqueness of weak solutions to the auxiliary problems derived from the main problem are investigated. </p><p> <b> DOI</b> 10.1134/S1061920824030154 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"544 - 561"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409601","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
Exponential Localization for Eigensections of the Bochner–Schrödinger operator 波赫纳-薛定谔算子等差数列的指数定位
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030099
Yu.A. Kordyukov
{"title":"Exponential Localization for Eigensections of the Bochner–Schrödinger operator","authors":"Yu.A. Kordyukov","doi":"10.1134/S1061920824030099","DOIUrl":"10.1134/S1061920824030099","url":null,"abstract":"<p> We study asymptotic spectral properties of the Bochner–Schrödinger operator <span>(H_{p}=frac 1pDelta^{L^potimes E}+V)</span> on high tensor powers of a Hermitian line bundle <span>(L)</span> twisted by a Hermitian vector bundle <span>(E)</span> on a Riemannian manifold <span>(X)</span> of bounded geometry under the assumption that the curvature form of <span>(L)</span> is nondegenerate. At an arbitrary point <span>(x_0)</span> of <span>(X)</span>, the operator <span>(H_p)</span> can be approximated by a model operator <span>(mathcal H^{(x_0)})</span>, which is a Schrödinger operator with constant magnetic field. For large <span>(p)</span>, the spectrum of <span>(H_p)</span> asymptotically coincides, up to order <span>(p^{-1/4})</span>, with the union of the spectra of the model operators <span>(mathcal H^{(x_0)})</span> over <span>(X)</span>. We show that, if the union of the spectra of <span>(mathcal H^{(x_0)})</span> over the complement of a compact subset of <span>(X)</span> has a gap, then the spectrum of <span>(H_{p})</span> in the gap is discrete, and the corresponding eigensections decay exponentially away from a compact subset. </p><p> <b> DOI</b> 10.1134/S1061920824030099 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"461 - 476"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409602","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 Uniform Structure of (mathfrak{g}^{otimes 4}) 的统一结构
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030038
M. Avetisyan, A.P. Isaev, S.O. Krivonos, R. Mkrtchyan
{"title":"The Uniform Structure of (mathfrak{g}^{otimes 4})","authors":"M. Avetisyan,&nbsp;A.P. Isaev,&nbsp;S.O. Krivonos,&nbsp;R. Mkrtchyan","doi":"10.1134/S1061920824030038","DOIUrl":"10.1134/S1061920824030038","url":null,"abstract":"<p> We obtain a uniform decomposition into Casimir eigenspaces (most of which are irreducible) of the fourth power of the adjoint representation <span>(mathfrak{g}^{otimes 4})</span> for all simple Lie algebras. We present universal, in Vogel’s sense, formulas for the dimensions and split Casimir operator’s eigenvalues of all terms in this decomposition. We assume that a similar uniform decomposition into Casimir eigenspaces with universal dimension formulas exists for an arbitrary power of the adjoint representations. </p><p> <b> DOI</b> 10.1134/S1061920824030038 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"379 - 388"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409620","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 Condition for the Strong Continuity of Representations of Topological Groups in Reflexive Fréchet Spaces 反身弗雷谢特空间中拓扑群表征的强连续性条件
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S106192082403018X
A.I. Shtern
{"title":"A Condition for the Strong Continuity of Representations of Topological Groups in Reflexive Fréchet Spaces","authors":"A.I. Shtern","doi":"10.1134/S106192082403018X","DOIUrl":"10.1134/S106192082403018X","url":null,"abstract":"<p> Some necessary and sufficient conditions for the strong continuity of representations of topological groups in reflexive Fréchet spaces are obtained. </p><p> <b> DOI</b> 10.1134/S106192082403018X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"571 - 573"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409610","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
Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities 具有 KPZ 非线性的季霍诺夫型反应-扩散-平流系统中周期抛物问题的解的存在性和渐近稳定性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030129
E.I. Nikulin, N.N. Nefedov, A.O. Orlov
{"title":"Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities","authors":"E.I. Nikulin,&nbsp;N.N. Nefedov,&nbsp;A.O. Orlov","doi":"10.1134/S1061920824030129","DOIUrl":"10.1134/S1061920824030129","url":null,"abstract":"<p> This paper studies time-periodic solutions of singularly perturbed Tikhonov systems of reaction–diffusion–advection equations with nonlinearities that include the square of the gradient of the unknown function (KPZ nonlinearities). The boundary layer asymptotics of solutions are constructed for Neumann and Dirichlet boundary conditions. The study considers both the case of quasimonotone sources and systems without the quasimonotonicity condition. The asymptotic method of differential inequalities is used to prove theorems on the existence of solutions and their Lyapunov asymptotic stability. </p><p> <b> DOI</b> 10.1134/S1061920824030129 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"504 - 516"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409641","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
Explicit Solution to the Birman Problem for the 2D-Laplace Operator 二维拉普拉斯算子的比尔曼问题的显式求解
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030117
M. Malamud
{"title":"Explicit Solution to the Birman Problem for the 2D-Laplace Operator","authors":"M. Malamud","doi":"10.1134/S1061920824030117","DOIUrl":"10.1134/S1061920824030117","url":null,"abstract":"<p> We construct an appropriate restriction of the 2-dimensional Laplace operator that has compact preresolvent though the resolvent of its Friedrichs extension is not compact and, moreover, its spectrum is absolutely continuous. This result solves the Birman problem. </p><p> <b> DOI</b> 10.1134/S1061920824030117 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"495 - 503"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409599","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 Point Spectrum of a Non-Self-Adjoint Quasiperiodic Operator 论非自交准周期算子的点谱
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S106192082403004X
D.I. Borisov, A.A. Fedotov
{"title":"On the Point Spectrum of a Non-Self-Adjoint Quasiperiodic Operator","authors":"D.I. Borisov,&nbsp;A.A. Fedotov","doi":"10.1134/S106192082403004X","DOIUrl":"10.1134/S106192082403004X","url":null,"abstract":"<p> We consider a difference operator acting in <span>(l^2(mathbb Z))</span> by the formula <span>(( mathcal{A} psi)_n=psi_{n+1}+psi_{n-1}+lambda e^{-2pi mathrm{i} (theta+omega n)} psi_n)</span>, <span>(nin mathbb{Z})</span>, where <span>(omegain(0,1))</span>, <span>(lambda&gt;0)</span>, and <span>(thetain [0,1])</span> are parameters. This operator was introduced by P. Sarnak in 1982. For <span>(omeganotin mathbb Q)</span>, the operator <span>( mathcal{A} )</span> is quasiperiodic. Previously, within the framework of a renormalization approach (monodromization method), we described the location of the spectrum of this operator. In the present work, we first establish the existence of the point spectrum for different values of parameters, and then study the eigenfunctions. To do so, using ideas of the renormalization approach, we study the difference operator on the circle obtained from the original one by the Fourier transform. This allows us, first, to obtain a new type condition guaranteeing the existence of point spectrum and, second, to describe in detail a multi-scale self-similar structure of the Fourier transforms of the eigenfunctions. </p><p> <b> DOI</b> 10.1134/S106192082403004X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"389 - 406"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409589","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 Higher Integrability of Solutions to the Poisson Equation with Drift in Domains Perforated Along the Boundary 论沿边穿孔域中有漂移的泊松方程解的高积分性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030051
G.A. Chechkin, T.P. Chechkina
{"title":"On Higher Integrability of Solutions to the Poisson Equation with Drift in Domains Perforated Along the Boundary","authors":"G.A. Chechkin,&nbsp;T.P. Chechkina","doi":"10.1134/S1061920824030051","DOIUrl":"10.1134/S1061920824030051","url":null,"abstract":"<p> In the paper, we consider a linear second order elliptic problem with drift in a domain perforated along the boundary. Setting homogeneous Dirichlet condition on the boundary of the cavities and homogeneous Neumann condition on the outer boundary of the domain, we prove the higher integrability of the gradient of the solution to the problem (the Boyarsky–Meyers estimate). </p><p> <b> DOI</b> 10.1134/S1061920824030051 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"407 - 417"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409590","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
Maslov Rank Distributions for the Analysis of Two-Dimensional and Quasi-Two-Dimensional Turbulent Flows 用于分析二维和准二维湍流的马斯洛夫秩分布
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030075
M.A. Guzev, S.V. Fortova, A.N. Doludenko, A.O. Posudnevskaya, A.D. Ermakov
{"title":"Maslov Rank Distributions for the Analysis of Two-Dimensional and Quasi-Two-Dimensional Turbulent Flows","authors":"M.A. Guzev,&nbsp;S.V. Fortova,&nbsp;A.N. Doludenko,&nbsp;A.O. Posudnevskaya,&nbsp;A.D. Ermakov","doi":"10.1134/S1061920824030075","DOIUrl":"10.1134/S1061920824030075","url":null,"abstract":"<p> A new practice of applying V.P. Maslov’s theoretical results has been implemented for analyzing fluid flow regimes that arise during their numerical modelling. In this paper, using the example of a Kolmogorov-type flow for two-dimensional motion of a viscous fluid, a rank analysis of the vorticity field and its frequency of occurrence is proposed. A similar analysis has been performed for the problem of forming columnar structures in the spatial case. It has been shown that, for the turbulent, vortex, and laminar fluid motion regimes, the rank distributions exhibit characteristics that can be used to classify the flow types. </p><p> <b> DOI</b> 10.1134/S1061920824030075 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"438 - 449"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409591","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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