148 research outputs found
Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces
We consider the Cauchy problem for the incompressible Navier-Stokes equations
in for a one-parameter family of explicit scale-invariant
axi-symmetric initial data, which is smooth away from the origin and invariant
under the reflection with respect to the -plane. Working in the class of
axi-symmetric fields, we calculate numerically scale-invariant solutions of the
Cauchy problem in terms of their profile functions, which are smooth. The
solutions are necessarily unique for small data, but for large data we observe
a breaking of the reflection symmetry of the initial data through a
pitchfork-type bifurcation. By a variation of previous results by Jia &
\v{S}ver\'ak (2013) it is known rigorously that if the behavior seen here
numerically can be proved, optimal non-uniqueness examples for the Cauchy
problem can be established, and two different solutions can exists for the same
initial datum which is divergence-free, smooth away from the origin, compactly
supported, and locally -homogeneous near the origin. In particular,
assuming our (finite-dimensional) numerics represents faithfully the behavior
of the full (infinite-dimensional) system, the problem of uniqueness of the
Leray-Hopf solutions (with non-smooth initial data) has a negative answer and,
in addition, the perturbative arguments such those by Kato (1984) and Koch &
Tataru (2001), or the weak-strong uniqueness results by Leray, Prodi, Serrin,
Ladyzhenskaya and others, already give essentially optimal results. There are
no singularities involved in the numerics, as we work only with smooth profile
functions. It is conceivable that our calculations could be upgraded to a
computer-assisted proof, although this would involve a substantial amount of
additional work and calculations, including a much more detailed analysis of
the asymptotic expansions of the solutions at large distances.Comment: 31 pages, 19 figure
Design of single-purpose machine for washer stamping
Tato bakalářská práce se věnuje návrhu a konstrukci jednoúčelového stroje pro zalisování podložek. Je popsán rozbor výrobní operace, navrhnuto řešení a zvoleny technické parametry stroje. Dále je v CAD systému tento stroj navrhnut, jsou provedeny základní konstrukční výpočty a je zdůvodněna volba nakupovaných dílů.This bachelor’s thesis deals with design and construction of single-purpose machine for washer stamping. Manufacturing operation is described, solution is suggested and technical parameters of machine are selected. Then machine is designed in CAD system, basic construct calculations are performed and choice of purchased parts is justified.
Influence of thermal insulation on the building proposal heat
Tato diplomová práce se zabývá vlivem zateplení objektu na návrh zdroje tepla. Teoretická část popisuje historický vývoj stavebnictví, počátky zateplování a základní pojmy spojené s výpočtem tepelných ztrát. V úvodu praktické části jsou popsány možné způsoby návrhu vytápění a stavebně-technický popis novostavby bytového domu Cacovická. Hlavní část řeší „Vliv zateplení na návrh zdroje tepla“, který je proveden ve dvou odlišných variantách. Závěrem práce je porovnání obou variant a vyhodnocení nákladově nižší varianty.This thesis deals with the influence of building insulation to design of the heat source. The theoretical part describes the historici evolution of the construction, insulation origins and basic concepts associated with heat loss calculations. Introduction to the practical part describes possible wals of rating proposal and construction and technical description of the new residential building Cacovická. The main part deals with "Influence of thermal insulation on the building proposal heat" performed in two different variants. Finally work is a comparison of the two variants and evaluation of lower cost options.
Liouville theorems in unbounded domains for the time-dependent Stokes system
In this paper, We characterize bounded ancient solutions to the
time-dependent Stokes system with zero boundary value in various domains,
including the half space.Comment: 11 pages; final versio
A stability result for nonlinear Neumann problems under boundary variations
In this paper we study, in dimension two, the stability of the solutions of
some nonlinear elliptic equations with Neumann boundary conditions, under
perturbations of the domains in the Hausdorff complementary topology.Comment: 26 page
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