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Double-deck structure of the boundary layer in the flow around a small localized irregularity on a curved surface
Russian Journal of Mathematical Physics. 2025. Vol. 32. No. 3. P. 458–463.
Equations of the double-deck boundary layer structure
are obtained in the problem of a flow of a viscous incompressible fluid
around a small irregularity on a curved surface at high Reynolds numbers.
It is shown that due to the chosen coordinate system,
the form of the equations of the double-deck structure
coincides with the previously studied case of a small irregularity
on a flat surface, the difference lies only in the values of the coefficients.
This means that the results of flow modeling for the flat case
can be qualitatively transferred to the curvilinear case.
Publication based on the results of:
Guterman A., Jonoska N., Kreines E. et al., Proceedings of the Edinburgh Mathematical Society 2026 Vol. 69 No. 3 P. 1041–1057
We provide four equivalent combinatorial conditions for a simple assembly graph (rigid vertex graph where all vertices are of degree 1 or 4) to have the largest number of Hamiltonian sets of polygonal paths relative to its size. These conditions serve to prove the conjecture that such a maximum, which is equal to 𝐹_(2𝑛+1) −1, ...
Added: September 27, 2026
Shishkina E., Современная математика. Фундаментальные направления 2026 Т. 72 № 1 С. 52–67
In this paper, we construct a weighted Sobolev space of fractional order based on the
generalized Bessel potential.We apply these results to the analysis of the singular fractional Schr¨odinger
equation. To solve the Cauchy problem for this equation, we prove an estimate that relates the norm of
the solution to the norm of the initial condition in the ...
Added: September 26, 2026
Shishkina E., Computational Mathematics and Mathematical Physics 2026 Vol. 66 No. 5 P. 804–815
This article demonstrates that the Laplace–Bessel operator generates a strongly continuous
semigroup on a weighted Lebesgue space. Using this semigroup, we define the fractional Laplace–
Bessel operator via Balakrishnan’s formula. Furthermore, we derive three distinct representations for
fractional powers of the negative Laplace–Bessel operator. ...
Added: September 26, 2026
Kolokoltsov V., Shishkina E., Journal of Theoretical Probability 2026 P. 39–83
In this paper, we introduce a new construction of fractional derivatives and integrals
with respect to a function, based on a matrix approach. We believe that this is a powerful
tool in both analytical and numerical calculations.We begin with the differential
operator with respect to a function that generates a semigroup. By discretizing this
operator, we obtain a matrix ...
Added: September 26, 2026
Petr Kucheriaviy, Bulletin of the Australian Mathematical Society 2026
We prove that an analogue of Rogers’ theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals. ...
Added: September 25, 2026
Пелевин Ф. Е., Математические заметки 2026 Т. 120 № 1 С. 159–163
Две не равные тождественно нулю функции (последовательности элементов некоторого поля) будем называть эквивалентными, если они удовлетворяют функциональному уравнению типа теорем сложения тэта-функций. Основной результат работы состоит в том, что рассматриваемое отношение действительно является отношением эквивалентности. ...
Added: September 25, 2026
Shimanogov I. N., Vyalyi M., Siberian Mathematical Journal 2026 Vol. 67 No. 5 P. 1203–1212
We consider a class of Boolean algebras formed by intersections of regular languages with
a given language. In the case where such an algebra is isomorphic to the algebra of regular languages,
we prove the existence of an isomorphism that is computable using oracles for the regular realizability
problem and the infinite regular realizability problem. This result yields ...
Added: September 25, 2026
Ramazanov I., Bukh A., Shepelev Igor A., Chaos 2026 No. 36 P. 083150–083150
We investigate how stochastic Poisson impulsive forcing influences the spatiotemporal dynamics of a two-dimensional network of Hindmarsh–Rose neurons. Unlike continuous noise, impulsive forcing introduces discrete, state-dependent perturbations, making the system response highly sensitive to both the statistics and the spatial structure of the input. In most of the parameter space, stochastic impulses destabilize the initial ...
Added: September 24, 2026
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Sokolov V., Adler V. E., Journal of Geometry and Physics 2026 Vol. 227 Article 105860
The group reduction procedure is applied to vector generalizations of the NLS, mKdV,
and KdV equations. The resulting ODE systems admit isomonodromic Lax representations
and are multicomponent generalizations of the Painlevé equations P 1, P 2, P 34, and P 4.
Some of them can be interpreted as nonautonomous deformations of well-known systems
integrable in the Liouville sense, in ...
Added: September 24, 2026
Sokolov V., BALAKHNEV M. Y., Ufa Mathematical Journal 2026 Vol. 18 No. №3 P. 85–93
A collection of miscellaneous continuous, semi-discrete, and discrete integrable
systems can be associated with each integrable evolution equation of the KdV type. We provide them for the Schwarz — KdV equation and generalize to the vector case. The existence
of these vector generalizations is a non-trivial found fact, no mathematical explanation of
which is known yet. ...
Added: September 24, 2026
Yakovlev E., Maksimov D. A., Mathematical notes 2026 Vol. 120 No. 3 P. 483–496
Smooth principal bundles whose total spaces and bases are time oriented Lorentzian manifolds and whose projections are Lorentzian submersions preserving time orientations are studied. Previously, the authors showed that the chronologicity, causality, and stable causality always lift from the base to the space of a Lorentzian bundle. For strong causality and global hyperbolicity, this holds ...
Added: September 24, 2026
Sokolov V., Shabat G. B., Tsiganov A. V., Journal of Geometry and Physics 2026 Vol. 220
We consider Novikov equations for commutative ring generated by differential operators of
orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method
of compatible Poisson brackets, we find a separation of variables on a hyperelliptic curve
of genus 2 for the Novikov equations ...
Added: September 24, 2026
Marshakov A., Yung A., Ievlev E. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 No. 114 P. 1–22
We continue the study of non-Abelian vortex string in 4D N ¼ 2 supersymmetric QCD (SQCD) as critical superstring, and extend this analysis to UðNÞ gauge theory with arbitrary even N and Nf ¼ 2N number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by ...
Added: September 24, 2026
Demina M.V., Nechitailo V., Analysis and Mathematical Physics 2026 Vol. 16 No. 5 P. 1–25
We present a method of finding non-Liouvillian first integrals of rational two-dimensional differential systems. The method is based on the existence of two independent invariants that satisfy a linear second-order ordinary differential equation with respect to one of the variables. We call systems with this property R-integrable. These invariants are not necessarily polynomial; they can ...
Added: September 24, 2026
Bitter I., Konakov V., Mathematical notes 2026 Vol. 120 No. 4 P. 599–615
The paper provides a generalization of the local limit theorem on the convergence
of inhomogeneous Markov chains to the diffusion limit for the case in which the corresponding
coefficients of the process satisfy weak regularity conditions and coincide only asymptotically.
In particular, the drift coefficients under consideration can be unbounded with at most linear
growth, and the bounds reflect ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Gaydukov R. K., Indian Journal of Pure and Applied Mathematics 2026 Vol. 57 No. 3 P. 808–825
The paper is deals with the heat transfer in the laminar flow of a viscous incompressible fluid along a plate with a small heated localized irregularity. It is well known that double- and triple-deck structures of the boundary layer arise in such flow problems. These structures make it possible, among other things, to describe the phenomenon of ...
Added: May 21, 2024
R. K. Gaydukov, Russian Journal of Mathematical Physics 2024 Vol. 31 No. 2 P. 209–217
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 non-symmetric irregularity localized on the disk surface. The results of numerical simulation of the flow near the surface are presented. The differences ...
Added: April 18, 2024
Gaydukov R., Сибирские электронные математические известия 2024 Т. 21 № 1 С. 178–187
In this paper we study a Rayleigh-type equation on a semi-infinite cylinder with a Coulomb-type potential.
This equation arises in the double-deck boundary layer structure in the problem of flow induced by a uniformly rotating disk with small periodic irregularities on its surface for large Reynolds numbers. Using combined numerical and analytical approach, the existence of ...
Added: February 17, 2024
R. K. Gaydukov, V. G. Danilov, Computational Mathematics and Mathematical Physics 2024 Vol. 64 No. 6 P. 1317–1325
Mathematical modeling of the ice–water phase transition during liquid flow inside a pipe
with a small ice buildup on the wall at high Reynolds numbers is considered. As a mathematical model
describing the dynamics of the phase transition, a double-deck boundary layer model and a phase field
system are used. Results of numerical simulation are presented. ...
Added: February 17, 2024
Gaydukov R., Russian Journal of Nonlinear Dynamics 2024 Vol. 20 No. 1 P. 113–125
The problem of flow of a non-Newtonian viscous fluid with power-law rheological properties
along a semi-infinite plate with a small localized irregularity on the surface is considered for large
Reynolds numbers. The asymptotic solution with double-deck structure of the boundary layer is
constructed. The numerical simulation of the flow in the region near the surface was performed
for different ...
Added: December 26, 2023
Danilov V., Gaydukov R., Russian Journal of Mathematical Physics 2023 Vol. 30 No. 2 P. 165–175
In this paper, we construct and study a model of a phase transition in a system of two
phases (liquid and ice) and three media — water, a piece of ice, and some nonmeltable
solid substrate. Namely, the melting-crystallization process is considered in the problem
of water flow along a small ice irregularity (such as a frozen drop) ...
Added: December 14, 2022
Gaydukov R., Fonareva A. V., European Journal of Mechanics - B/Fluids 2022 Vol. 94 P. 50–59
The problem of a rotating disk with slightly perturbed surface immersed in a viscous fluid is considered.
The asymptotic solutions with double-deck structure of the boundary layer are constructed for symmetric
periodic and localized types of irregularities on the disk surface for large Reynolds numbers. The paper
presents the results of numerical simulations of the flow near the ...
Added: November 14, 2021