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The Muskat problem and related topics
Lithuanian Mathematical Journal. 2018. Vol. 58. P. 284–308.
Meirmanov A. M., Galtsev O. V.
In the paper, we consider the evolution of the free boundary separating two immiscible viscous fluids with different constant densities in an absolutely rigid solid body and in an elastic skeleton. The motion of the liquids is described by the Stokes equations driven by the input pressure and the force of gravity. For flows in a bounded domain, we prove the existence and uniqueness of classical solutions and emphasize the study of the properties of the moving boundary separating the two fluids.
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Королев А. В., Koroleva Y., Buletinul Academiei de Ştiinţe a Republicii Moldova 2021 No. 1-2 P. 31–68
In present paper we do a homogenization with respect to a small parameter of a boundary-value problem describing fluid flow between two moving in space and time rough surfaces. The two-scale convergence method was used to justify the behavior of the flow in the limit. ...
Added: July 7, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Losev A., Filyaev A., Zavodilenko V. V. et al., Sensors 2026 Vol. 26 No. 4 P. 1228
A 2D model of an InGaAs/InAlAs single-photon avalanche photodiode has been developed. The influence of the active area structure in the multiplication region on the diode’s operating parameters has been studied. It was found that changing the diameter of the structure’s active region leads to a change in the dark current in the linear part ...
Added: May 6, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Didenkulova E., Flamarion M., Pelinovsky E., Physica D: Nonlinear Phenomena 2025 Vol. 481 Article 134815
A comparison of the statistical characteristics of a rarefied soliton gas is carried out within the framework of integrable and non-integrable equations from the Korteweg-de Vries (KdV) hierarchy. As examples, multi-soliton solutions of the modified KdV equation, and the modular Schamel equation are considered. A common property of the dynamics of bipolar solitons is the ...
Added: March 11, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
He Y., Slunyaev A., Mori N. et al., Physica D: Nonlinear Phenomena 2026 Vol. 488 Article 135098
Extreme wave localizations in nonlinear dispersive media, arising from modulation instability in weakly nonlinear
wave interactions, can be effectively modeled by breather solutions. These breathers are exact solutions
of the nonlinear Schrödinger equation and provide accurate models for understanding and controlling unidirectional
rogue wave dynamics in numerical simulations or laboratory settings. A recent study by Y. He et ...
Added: February 12, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Perov G. A., Presnyakov S., Kasatkin A. et al., , in: 2025 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO).: IEEE, 2025.
It is generally recognised that communication is one of the most important areas of technology. Moreover, the study and improvement of amplification devices operating in little-studied frequency ranges is an essential part of the modern communication development. This work is aimed at investigating the electrodynamic properties of modified designs of helix slow-wave systems, used in ...
Added: December 15, 2025
Flamarion M. V., E. Pelinovsky, E. Didenkulova, Physics of Wave Phenomena 2025 Vol. 33 No. 1 P. 9–19
The present paper is devoted to the study of the dynamics of narrowband wave fields within the
nonintegrable Schamel equation, which plays an important role in plasma physics, wave dynamics in metamaterials,
and electrical circuits. A Monte Carlo approach is used to obtain a large number of random independent
realizations of the wave fields, allowing for an investigation ...
Added: March 23, 2025
Kuznetsova A., Байдаков Г. А., Троицкая Ю. И., Izvestia, Atmospheric and Oceanic Physic 2024 Vol. 60 No. 3 P. 306–319
This paper provides an overview of a series of papers aimed at creating a regional model based on the WAVEWATCH III spectral wave model adapted to conditions of an inland water body using the WRF atmospheric model. The models are adapted and verified based on results of a series of full-scale experiments on studying the wind–wave ...
Added: December 6, 2024
Сехлеян С. А., Социология. Журнал Российской социологической ассоциации 2021 № 5 С. 165–170
CULTURAL GLOBALIZATION: HOMOGENIZATION AND HYBRIDIZATION SCENARIOS
The phenomenon of globalization is a process that affects the material and spiritual aspects of life - economics, demography and politics, as well as culture. Based on this, globalization is an object of study not only in social sciences, but also in branches of knowledge - economics, politics, international relations ...
Added: July 16, 2024