共查询到20条相似文献,搜索用时 265 毫秒
1.
J. L. Boldrini M. Poblete-Cantellano L. Friz M. A. Rojas-Medar 《Numerical Functional Analysis & Optimization》2016,37(3):304-323
The goal of this article is to present pointwise time error estimates in suitable Hilbert spaces by considering spectral Galerkin approximations of the micropolar fluid model for strong solutions. In fact, we use the properties of the Stokes and Lamé operators for prove the pointwise convergence rate in the H2-norm for the ordinary velocity and microrotational velocity and the pointwise convergence rate in the L2-norm for the time-derivative of both velocities. The novelty of our method is that we do not impose any compatibility conditions in the initial data. 相似文献
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In this paper, we consider one‐dimensional compressible viscous and heat‐conducting micropolar fluid, being in a thermodynamical sense perfect and polytropic. The homogenous boundary conditions for velocity, microrotation, and temperature are introduced. This problem has a global solution with a priori estimates independent of time; with the help of this result, we first prove the exponential stability of solution in (H1(0,1))4, and then we establish the global existence and exponential stability of solutions in (H2(0,1))4 under the suitable assumptions for initial data. The results in this paper improve those previously related results. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Takayuki Kubo 《Mathematical Methods in the Applied Sciences》2005,28(11):1341-1357
We shall construct a periodic strong solution of the Navier–Stokes equations for some periodic external force in a perturbed half‐space and an aperture domain of the dimension n?3. Our proof is based on Lp–Lq estimates of the Stokes semigroup. We apply Lp–Lq estimates to the integral equation which is transformed from the original equation. As a result, we obtain the existence and uniqueness of periodic strong solutions. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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L. C. F. Ferreira E. J. Villamizar‐Roa 《Mathematical Methods in the Applied Sciences》2007,30(10):1185-1208
We prove the existence of a global strong solution in some class of Marcinkiewicz spaces for the micropolar fluid in an exterior domain of R3, with initial conditions being a non‐smooth disturbance of a steady solution. We also analyse the large time behaviour of those solutions and apply our results in the context of the Navier–Stokes equations. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
8.
E.E. Ortega‐Torres M.A. Rojas‐Medar R.C. Cabrales 《Numerical Methods for Partial Differential Equations》2012,28(2):689-706
We consider Galerkin approximations for the equations modeling the motion of an incompressible magneto‐micropolar fluid in a bounded domain. We derive an optimal uniform in time error bound in the H1 and L2 ‐norms for the velocity. This is done without explicit assumption of exponential stability for a class of solutions corresponding to decaying external force fields. Our study is done for no‐slip boundary conditions, but the results obtained are easily extended to the case of periodic boundary conditions. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 689–706, 2012 相似文献
9.
Piotr Szopa 《Mathematical Methods in the Applied Sciences》2010,33(13):1587-1595
This paper is devoted to obtain ladder inequalities for 2D micropolar fluid equations on a periodic domain Q=(0, L)2. The ladder inequalities are differential inequalities that connect the evolution of L2 norms of derivatives of order N with the evolution of the L2 norms of derivatives of other (usually lower) order. Moreover, we find (with slight assumption on external fields) long‐time upper bounds on the L2 norms of derivatives of every order, which implies that a global attractor is made up from C∞ functions. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
10.
Markus Stoth 《Mathematical Methods in the Applied Sciences》1996,19(1):15-31
We analyse the time decay of solutions to the Cauchy problem for the linear hyperbolic system of elasticity for anisotropic media. As an example, we will consider media with hexagonal symmetry. First we derive decay estimates for special initial data using the method of stationary phase in several variables and degenerate phase function based on the Malgrange preparation theorem. Asymptotic expansions are given to prove the sharpness of the weaker time decay found for zinc and beryl than in the isotropic case. A method using Besov spaces leads to ℒ︁p–ℒ︁q-estimates. 相似文献
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We prove existence, uniqueness and exponential stability of stationary Navier–Stokes flows with prescribed flux in an unbounded cylinder of ?n,n?3, with several exits to infinity provided the total flux and external force are sufficiently small. The proofs are based on analytic semigroup theory, perturbation theory and Lr ? Lq‐estimates of a perturbation of the Stokes operator in Lq‐spaces. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
12.
Fabio Punzo 《Journal of Evolution Equations》2012,12(3):571-592
We are concerned with existence, uniqueness and nonuniqueness of nonnegative solutions to the semilinear heat equation in open subsets of the n-dimensional sphere. Existence and uniqueness results are obtained using L p ?? L q estimates for the semigroup generated by the Laplace?CBeltrami operator. Moreover, under proper assumptions on the nonlinear function, we establish nonuniqueness of weak solutions, when n??? 3; to do this, we shall prove uniqueness of positive classical solutions and nonuniqueness of singular solutions of the corresponding semilinear elliptic problem. 相似文献
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We prove a theorem about global existence (in time) of the solution to the initial‐value problem for a nonlinear hyperbolic parabolic system of coupled partial differential equation of second order describing the process of thermodiffusion in solid body. The corresponding global existence theorems has been proved using the Lp ‐ Lq time decay estimates for the solution of the associated linearized problem. Next, we proved the energy estimate in the Sobolev space with constant independent of time. Such an energy estimate allows us to apply the standard (continuation argument and to continue the local solution to one de.ned for all t ∈ 〈0, ∞)). 相似文献
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We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov's method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L1 for entropy solutions. To prove the existence we use the nonlinear semigroup theory and we show that when the initial and boundary data are nonnegative the semigroup solutions are strong solutions. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(3):233-238
Consider the non-autonomous initial value problem u′(t) + A(t)u(t) = f(t), u(0) = 0, where −A(t) is for each t [0,T], the generator of a bounded analytic semigroup on L2(Ω). We prove maximal Lp — Lq a priori estimates for the solution of the above equation provided the semigroups Tt are associated to kernels which satisfies an upper Gaussian bound and A(t), t [0, T] fulfills a Acquistapace-Terreni commutator condition. 相似文献
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Michael Dreher 《Journal of Evolution Equations》2009,9(4):829-844
We study mixed order parameter-elliptic boundary value problems with boundary conditions of a certain structure. For such
operators, we prove resolvent estimates in L
p
based Sobolev spaces of suitable order and the analyticity of the semigroup. Finally, we present an application of this theory
to studies of the particle transport in a semi-conductor. 相似文献
17.
In an exterior domain Ω??n, n ? 2, we consider the generalized Stokes resolvent problem in Lq-space where the divergence g = div u and inhomogeneous boundary values u = ψ with zero flux ∫?Ωψ·N do = 0 may be prescribed. A crucial step in our approach is to find and to analyse the right space for the divergence g. We prove existence, uniqueness and a priori estimates of the solution and get new results for the divergence problem. Further, we consider the non-stationary Stokes system with non-homogeneous divergence and boundary values and prove estimates of the solution in L5(0, T;Lq(Ω)) for 1 < s, q < ∞. 相似文献
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Yu. A. Kordyukov 《Acta Appl Math》1991,23(3):223-260
This paper is devoted to some of the properties of uniformly elliptic differential operators with bounded coefficients on manifolds of bounded geometry in L
pspaces. We prove the coincidence of minimal and maximal extensions of an operator of a considered type with a positive principal symbol, the existence of holomorphic semigroup, generated by it, and the estimates of L
p-norms of the operators of this semigroup. Some spectral properties of such operators in L
pspaces are also studied. 相似文献
19.
Mahdi Boukrouche Grzegorz ukaszewicz 《Mathematical Methods in the Applied Sciences》2005,28(14):1673-1694
This research is motivated by a problem from lubrication theory. We consider a free boundary problem of a two‐dimensional boundary‐driven micropolar fluid flow. The existence of a unique global‐in‐time solution of the problem and the global attractor for the associated semigroup are known. In this paper we estimate the dimension of the global attractor in terms of the given data and the geometry of the domain of the flow by establishing a new version of the Lieb–Thirring inequality with constants depending explicitly on the geometry of the domain. We also obtain some new estimates for the Navier–Stokes shear flows. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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Koumei Tanaka 《Mathematical Methods in the Applied Sciences》2006,29(12):1451-1466
We consider a compressible viscous fluid with the velocity at infinity equal to a strictly non‐zero constant vector in ?3. Under the assumptions on the smallness of the external force and velocity at infinity, Novotny–Padula (Math. Ann. 1997; 308 :439– 489) proved the existence and uniqueness of steady flow in the class of functions possessing some pointwise decay. In this paper, we study stability of the steady flow with respect to the initial disturbance. We proved that if H3‐norm of the initial disturbance is small enough, then the solution to the non‐stationary problem exists uniquely and globally in time, which satisfies a uniform estimate on prescribed velocity at infinity and converges to the steady flow in Lq‐norm for any number q? 2. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献