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Pierre Bousquet 《Journal d'Analyse Mathématique》2007,102(1):311-346
We are interested in the location of the singularities of maps u ∈ W
s,p
(S
N
, S
1) when 1 ≤ sp and 1 < sp < 2. To this end, we consider the distributional Jacobian. We show that the range of this operator on W
s,p
(S
N
, S
1) is the closure in W
s−2,p
⋂ W
−1,sp
of the set of N − 2-currents defined as the integration on smooth oriented N − 2-dimensional boundaryless submanifolds. 相似文献
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R. V. Brizitskii 《Journal of Applied and Industrial Mathematics》2010,4(3):309-317
Under study are extremal problems for the stationary Navier-Stokes equations with mixed boundary conditions on velocity. Some
new a priori estimates are deduced for solutions to the extremal problems under consideration. These yield some local theorems
on the uniqueness and stability of solutions for the particular quality functionals that depend on the total pressure. 相似文献
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In this paper we prove an analog of the Luzin theorem on correction for spaces of the Sobolev type on an arbitrary metric
space with a measure, satisfying the doubling condition. The correcting function belongs to the H?lder class and approximates
a given function in the metrics of the initial space. Dimensions of exceptional sets are evaluated in terms of Hausdorff capacities
and volumes.
Original Russian Text ? V.G. Krotov and M.A. Prokhorovich, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika,
2008, No. 5, pp. 55–66.
Dedicated to the memory of Petr Lavrent’evich Ul’yanov 相似文献
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Assuming m − 1 < kp < m, we prove that the space C
∞(M, N) of smooth mappings between compact Riemannian manifolds M, N (m = dim M) is dense in the Sobolev space W
k,p
(M, N) if and only if π
m−1(N) = {0}. If π
m−1(N) ≠ {0}, then every mapping in W
k,p
(M, N) can still be approximated by mappings M → N which are smooth except in finitely many points. 相似文献
10.
In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f
n
(x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ℝ,G∈C
m
(J
n+1, ℝ) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces
and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence,
uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in
reference in different aspects. 相似文献
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Jörg Wolf 《Annali dell'Universita di Ferrara》2010,56(1):97-139
We consider suitable weak solutions to an incompressible viscous Newtonian fluid governed by the Navier-Stokes equations in the half space \({\mathbb {R}^3_+}\). Our main result is a direct proof of the partial regularity up to the flat boundary based on a new decay estimate, which implies the regularity in the cylinder \({Q_\rho ^+(x_0, t_0)}\) provided with ε 0 sufficiently small. In addition, we get a new condition for the local regularity beyond Serrin’s class which involves the L 2-norm of ?u and the L 3/2-norm of the pressure.
相似文献
$\limsup_{R\to 0}\frac {1} {R}\int\limits_{Q_R^+(x_0, t_0)} |{\rm rot}\,\mathbf u|^2 dxdt \,\leq\, \varepsilon _0$
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A. A. Ivanchikov 《Moscow University Mathematics Bulletin》2007,62(6):237-241
In order to stabilize an unstable solution to Navier-Stokes equations with the help of boundary conditions, a discrete analogue of the algorithm proposed by A. V. Fursikov in the differential case is constructed. A Quette flow between rotating cylinders is taken as an unstable solution. A complete calculation cycle of stabilization is performed and the obtained results are discussed 相似文献
16.
Changbing Hu 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):3964-3997
In this article, we study the spectrum of the Stokes operator in a 3D two layer domain with interface, obtain the asymptotic estimates on the spectrum of the Stokes operator as thickness ε goes to zero. Based on the spectral decomposition of the Stokes operator, a new average-like operator is introduced and applied to the study of Navier-Stokes equation in the two layer thin domains under interface boundary condition. We prove the global existence of strong solutions to the 3D Navier-Stokes equations when the initial data and external forces are in large sets as the thickness of the domain is small. This article is a continuation of our study on the Stokes operator under Navier friction boundary condition. Due to the viscosity distinction between the two layers, the Stokes operator displays radically different spectral structure from that under Navier friction boundary condition, then causes great difficulty to the analysis. 相似文献
17.
In unbounded domains Ω of the three-dimensional Euclidean space, having several outlets Ω i i=1,...,N, at infinity, one investigates the time-dependent solutions of the Stokes and Navier-Stokes system of equations for incompressible fluids, equal to zero at the boundary of the domain Ω and having arbitrary flows ∝ i through each of the outlets Ωi (the numbers ∝ i satisfy only the necessary condition: \(\sum\limits_{i = 1}^N {\alpha _i } = 0\) ). For these solutions one establishes Phragmén-Lindelöf and Saint-Venant type theorems characterizing the growth of solutions at infinity. On their basis, one formulates well-posed boundary value problems for the above indicated systems and domain Ω and one proves their solvability for any quantities ∝ i . One investigates various properties of these solutions and one gives sufficient conditions for uniqueness theorems. In particular, when Ω is a pipe with cylindrical ends, then our solutions approach the Poiseuille flows with a given flow ∝ i , for any in the case of the Stokes system and for ∝ i smaller in absolute value than some critical value ∝ i * , in the case of the Navier-Stokes system. 相似文献
18.
G. V. Sandrakov 《Journal of Mathematical Sciences》2007,143(4):3377-3385
We prove statements on asymptotic estimates of solutions of nonstationary Navier-Stokes equations with periodic data rapidly
oscillating with respect to the spatial variables when the oscillations are zero in mean. A viscosity coefficient is also
considered as a positive parameter in the equations. In the general case, the proved estimates are realistic whenever the
viscosity coefficient is not too small in comparison with some power of the parameter specifying the period of data oscillations.
In particular, such estimates are valid for Kolmogorov flow with Reynolds number not too large. We formulate conditions under
which the asymptotics for velocity fields can contain rapidly oscillating terms.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 309–322, 2007. 相似文献
19.
Ryosuke Kodera 《Journal of Algebraic Combinatorics》2009,30(4):491-514
We generalize Benkart-Frenkel-Kang-Lee’s adjoint crystals and describe their crystal structure for type A
n
(1), C
n
(1) and D
n+1(2). 相似文献