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1.
Very weak solutions to the rotating Stokes,Oseen and Navier–Stokes problems in weighted spaces 下载免费PDF全文
S. Kračmar M. Krbec Š. Nečasová P. Penel K. Schumacher 《Mathematische Nachrichten》2016,289(11-12):1466-1487
We consider the linearized and nonlinear problems arising from the motion of fluid flow around a rotating rigid body. We are interested in very weak solutions of these problems. 相似文献
2.
Consider a viscous incompressible flow around a body in $\mathbb R^3$ rotating with constant angular velocity ω. Using a coordinate system attached to the body, the problem is reduced to a modified Navier‐Stokes system in a fixed exterior domain. This paper addresses the question of the asymptotic behavior of stationary solutions to the new system as |x| → ∞. Under a suitable smallness assumption on the velocity field, u, and the net force on the boundary, N, we prove that the leading term of u is the so‐called Landau solution U, a singular solution of the stationary Navier‐Stokes system in $\mathbb R^3$ with external force kωδ0 and decaying as 1/|x|; here $k\in \mathbb R$ is a suitable constant determined by N and δ0 is the Dirac measure supported in the origin. 相似文献
3.
4.
Katrin Schumacher 《Journal of Evolution Equations》2009,9(1):1-36
We investigate the solvability of the instationary Stokes equations with fully inhomogeneous data in , where is a Bessel-potential space with a Muckenhoupt weight w. Depending on the order of this Bessel-potential space we are dealing with strong solutions or with very weak solutions.
Whereas in the context of lowest regularity one obtains solvability with respect to inhomogeneous data by dualization, this
is more delicate in the case of higher regularity, where one has to introduce some additional time regularity. As a preparation,
we introduce a generalization of the Stokes operator that is appropriate to the context of very weak solutions in weighted
Bessel-potential spaces.
相似文献
5.
《Mathematische Nachrichten》2018,291(11-12):1781-1800
We show existence theorem of global mild solutions with small initial data and external forces in the time‐weighted Besov space which is an invariant space under the change of scaling. The result on local existence of solutions for large data is also discussed. Our method is based on the ‐ estimate of the Stokes equations in Besov spaces. Since we construct the global solution by means of the implicit function theorem, as a byproduct, its stability with respect to the given data is necessarily obtained. 相似文献
6.
F. Flandoli 《Journal of Evolution Equations》2006,6(2):269-286
3D stochastic Navier-Stokes equations with a suitable nondegenerate noise are considered. Following a method introduced by
Da Prato and Debussche, it is proved that every Markov process associated to the equations has a Strong Feller like continuity
property with respect to initial conditions.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
7.
We construct and justify the asymptotic representation at infinity of solutions to the Stokes problem in a three‐dimensional domain with periodic geometric structure, which is bounded in one dimension, e.g., a periodically perforated layer. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
8.
We consider the zero-velocity stationary problem of the Navier–Stokes equations of compressible isentropic flow describing
the distribution of the density ϱ of a fluid in a spatial domain Ω⊂ℝ
N
driven by a time-independent potential external force b=∇F. A sharp condition in terms of F is given for the problem to possess a unique nonnegative solution ϱ having a prescribed mass m > 0.
Received: 20 October 1997 相似文献
9.
We consider nonlinear elliptic equations of p -Laplacian type that are not necessarily of variation form when the nonlinearity is allowed to be discontinuous and the boundary of the domain can go beyond the Lipschitz category. Under smallness in the BMO nonlinearity and sufficient flatness of the Reifenberg domain, we obtain the global weighted Lq estimates with q∈(p,∞) for the gradient of weak solutions. 相似文献
10.
Takahiro Okabe 《Journal of Differential Equations》2009,246(2):895-908
We study the asymptotic behavior of the energy of weak solutions of Navier-Stokes equations as t→∞. We characterize the space of the initial data which causes a concentration of the kinetic energy in the phase space. Moreover, an explicit convergence rate is obtained. 相似文献
11.
Strong maximal operator and singular integral operators in weighted Morrey spaces on product domains
《Mathematische Nachrichten》2017,290(16):2629-2640
We introduce the Morrey spaces on product domains and extend the boundedness of strong maximal operator and singular integral operators on product domains to Morrey spaces. 相似文献
12.
Heinz-Otto Kreiss 《Journal of Differential Equations》2004,203(2):216-231
In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial velocity field. For illustrative purposes, we first derive corresponding a priori estimates for certain parabolic systems. Because of the pressure term, the case of the Navier-Stokes equations is more difficult, however. 相似文献
13.
Hans Triebel 《Mathematische Nachrichten》2015,288(8-9):1057-1072
The paper deals with global solutions of Navier‐Stokes equations with infrared‐damped initial data in the context of Haar wavelets and function spaces of type where . 相似文献
14.
Yachun Li Dongmei Feng Zejun Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(2):239-253
We are concerned with global entropy solutions to the relativistic Euler equations for a class of large initial data which involve the interaction of shock waves and rarefaction waves. We first carefully analyze the global behavior of the shock curves, the rarefaction wave curves, and their corresponding inverse curves in the phase plane. Based on these analyses, we use the Glimm scheme to construct global entropy solutions to the relativistic Euler equations for the class of large discontinuous initial data.Received: May 23, 2004 相似文献
15.
《Mathematische Nachrichten》2017,290(16):2524-2546
Consider the Stokes equations in a sector‐like C 3 domain . It is shown that the Stokes operator generates an analytic semigroup in for . This includes domains where the ‐Helmholtz decomposition fails to hold. To show our result we interpolate results of the Stokes semigroup in and L 2 by constructing a suitable non‐Helmholtz projection to solenoidal spaces. 相似文献
16.
We consider in this paper the relativistic Euler equations in isentropic fluids with the equation of state p = κ2ρ, where κ, the sound speed, is a constant less than the speed of light c. We discuss the convergence of the entropy solutions as c→∞. The analysis is based on the geometric properties of nonlinear wave curves and the Glimm’s method. 相似文献
17.
In this paper, we study solvability of the local mild solution of stochastic Navier‐Stokes equation with jump noise in ‐spaces. This research work has mainly carried out by exploiting some interesting works of Tosio Kato. 相似文献
18.
Alexei Yu. Karlovich 《Integral Equations and Operator Theory》2000,38(1):28-50
In this paper we extend necessary conditions for Fredholmness of singular integral operators with piecewise continuous coefficients in rearrangement-invariant spaces [19] to the weighted caseX(,w). These conditions are formulated in terms of indices (Q
t
w) and (Q
t
w) of a submultiplicative functionQ
t
w, which is associated with local properties of the space, of the curve, and of the weight at the pointt. Using these results we obtain a lower estimate for the essential norm |S| of the Cauchy singular integral operatorS in reflexive weighted rearrangement-invariant spacesX(,w) over arbitrary Carleson curves :
where
. In some cases we give formulas for computation of (Q
t
w) and (Q
t
w). 相似文献
19.
In this paper, some sufficient conditions in terms of the magnetic field are established to guarantee global existence of solutions to a magnetohydrodynamic‐omega model. 相似文献
20.
R. del Campo A. Fernández A. Manzano F. Mayoral F. Naranjo 《Mathematische Nachrichten》2014,287(1):23-31
We apply the Calderón interpolation methods to Orlicz and weakly Orlicz function spaces with respect to a Banach‐space‐valued measure defined on a σ‐algebra. The results we obtain generalize those in the case of Banach lattices of p‐integrable and weakly p‐integrable functions with respect to such a vector measure. 相似文献