We review several regularity criteria for the Navier-Stokes equations and prove some new ones, containing different components of the velocity gradient.
We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor , where the nonlinear function satisfies or . First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for for both models. Then, under vanishing higher viscosity , the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for , its uniqueness and...
We study steady flow of a compressible heat conducting viscous fluid in a bounded two-dimensional domain, described by the Navier-Stokes-Fourier system. We assume that the pressure is given by the constitutive equation , where is the density and is the temperature. For , we prove existence of a weak solution to these equations without any assumption on the smallness of the data. The proof uses special approximation of the original problem, which guarantees the pointwise boundedness of the...
We consider a model for the viscoelastic fluid which has recently been studied in [4] and [1]. We show the local-in-time existence of a strong solution to the corresponding system of partial differential equations under less regularity assumptions on the initial data than in the above mentioned papers. The main difference in our approach is the use of the theory for the Stokes system.
Článok sa zaoberá efektívnou integráciou moderných technológií do vzdelávacieho procesu na prvom stupni základných škôl. Autori článku charakterizujú interaktívne aplikácie, ktoré sú primárne určené na nácvik sčítania a odčítania. Tieto aplikácie, ktoré sú vhodné najmä pre žiakov prvého a druhého ročníka základnej školy, môžu byť využívané počas vyučovacích hodín matematiky v kombinácii s interaktívnou tabuľou, ale najmä pre samostatnú prácu žiakov, či už v rámci vyučovacích hodín, školských klubov...
We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law if and if , , depending on the model for the heat flux.
We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
We consider the steady plane flow of certain classes of viscoelastic fluids in exterior domains with a non-zero velocity prescribed at infinity. We study existence as well as asymptotic behaviour of solutions near infinity and show that for sufficiently small data the solution decays near infinity as fast as the fundamental solution to the Oseen problem.
A graph is called distance integral (or -integral) if all eigenvalues of its distance matrix are integers. In their study of -integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on -integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs with , and with , as well as the infinite classes of distance integral complete...
We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions.
We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like (p > 6/5), regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we prove global existence of a weak solution to the corresponding system of partial differential equations.
We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the ``back to coordinates map'' may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for...
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