共查询到20条相似文献,搜索用时 15 毫秒
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2.
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
3.
The purpose of this paper is to use semiclassical analysis to unify and generalize L
p estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates do not depend on ellipticity
and order, and apply to operators which are selfadjoint only at the principal level. They are estimates on weakly approximate
solutions to semiclassical pseudodifferential equations.
Submitted: May 11, 2006. Accepted: September 19, 2006. 相似文献
4.
Pierre‐Étienne Druet 《Mathematical Methods in the Applied Sciences》2009,32(2):135-166
Accurate modelling of heat transfer in high‐temperature situations requires accounting for the effect of heat radiation. In complex industrial applications involving dissipative heating, we hardly can expect from the mathematical theory that the heat sources will be in a better space than L1. In this paper, we focus on a stationary heat equation with nonlocal boundary conditions and Lp right‐hand side, with p?1 being arbitrary. Thanks to new coercivity results, we are able to produce energy estimates that involve only the Lp norm of the heat sources and to prove the existence of weak solutions. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
5.
Matti Schneider 《Mathematical Methods in the Applied Sciences》2015,38(13):2761-2778
The FFT‐based homogenization method of Moulinec–Suquet has recently attracted attention because of its wide range of applicability and short computational time. In this article, we deduce an optimal a priori error estimate for the homogenization method of Moulinec–Suquet, which can be interpreted as a spectral collocation method. Such methods are well‐known to converge for sufficiently smooth coefficients. We extend this result to rough coefficients. More precisely, we prove convergence of the fields involved for Riemann‐integrable coercive coefficients without the need for an a priori regularization. We show that our L2 estimates are optimal and extend to mildly nonlinear situations and Lp estimates for p in the vicinity of 2. The results carry over to the case of scalar elliptic and curl ? curl‐type equations, encountered, for instance, in stationary electromagnetism. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
6.
In Krylov (Journal of the Juliusz Schauder Center 4 (1994), 355–364), a parabolic Littlewood–Paley inequality and its application
to an L
p
-estimate of the gradient of the heat kernel are proved. These estimates are crucial tools in the development of a theory
of parabolic stochastic partial differential equations (Krylov, Mathematical Surveys and Monographs vol. 64 (1999), 185–242).
We generalize these inequalities so that they can be applied to stochastic integrodifferential equations.
相似文献
7.
Howard Swann 《Numerical Methods for Partial Differential Equations》2000,16(5):480-493
The cell discretization algorithm, a nonconforming extension of the finite element method, is used to obtain approximations to the velocity and pressure functions satisfying the Stokes equations. Error estimates show convergence of the method. An implementation using polynomial bases is described that permits the use of the continuous approximations of the h‐p finite element method and exactly satisfies the solenoidal requirement. We express the error estimates in terms of the diameter h of a cell and degree p of the approximation on each cell. Examples of 10th degree polynomial approximations are described that substantiate the theoretical estimates. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 480–493, 2000 相似文献
8.
《Mathematical Methods in the Applied Sciences》2018,41(10):3588-3604
We consider the periodic problem for 2‐fluid nonisentropic Euler‐Poisson equations in semiconductor. By choosing a suitable symmetrizers and using an induction argument on the order of the time‐space derivatives of solutions in energy estimates, we obtain the global stability of solutions with exponential decay in time near the nonconstant steady‐states for 2‐fluid nonisentropic Euler‐Poisson equations. This improves the results obtained for models with temperature diffusion terms by using the pressure functions pν in place of the unknown variables densities nν. 相似文献
9.
In this paper we prove Lp estimates (p≥2) for the uniform norm of the paths of solutions of quasilinear stochastic partial differential equations (SPDE) of parabolic
type. Our method is based on a version of Moser's iteration scheme developed by Aronson and Serrin in the context of non-linear
parabolic PDE. 相似文献
10.
Fengping Yao 《Mathematical Methods in the Applied Sciences》2011,34(13):1587-1593
In this paper, we obtain the global regularity estimates in Orlicz spaces for second‐order divergence elliptic and parabolic equations with BMO coefficients in the whole space. In fact, the global result can follow from the local estimates. As a corollary we obtain Lp‐type regularity estimates for such equations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
We derive interior L
p
-estimates for solutions of linear elliptic systems with oscillatory coefficients. The estimates are independent of ε, the small length scale of the rapid oscillations. So far, such results are based on potential theory and restricted to periodic
coefficients. Our approach relies on BMO-estimates and an interpolation argument, gradients are treated with the help of finite
differences. This allows to treat coefficients that depend on a fast and a slow variable. The estimates imply an L
p
-corrector result for approximate solutions.
相似文献
12.
Nicolas Saintier 《Calculus of Variations and Partial Differential Equations》2006,25(3):299-331
We prove the SH1p—theory for critical equations involving the p-Laplace operator on compact manifolds. We also prove pointwise estimates for
these equations. 相似文献
13.
We study Lp-viscosity solutions of fully nonlinear, second-order, uniformly elliptic partial differential equations (PDE) with measurable terms and quadratic nonlinearity. We present a sufficient condition under which the maximum principle holds for Lp-viscosity solution. We also prove stability and existence results for the equations under consideration. 相似文献
14.
This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory. 相似文献
15.
We consider the Cauchy problem for the system of semilinear damped wave equations with small initial data: We show that a critical exponent which classifies the global existence and the finite time blow up of solutions indeed coincides with the one to a corresponding semilinear heat systems with small data. The proof of the global existence is based on the Lp–Lq estimates of fundamental solutions for linear damped wave equations [K. Nishihara, Lp–Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application, Math. Z. 244 (2003) 631–649; K. Marcati, P. Nishihara, The Lp–Lq estimates of solutions to one-dimensional damped wave equations and their application to compressible flow through porous media, J. Differential Equations 191 (2003) 445–469; T. Hosono, T. Ogawa, Large time behavior and Lp–Lq estimate of 2-dimensional nonlinear damped wave equations, J. Differential Equations 203 (2004) 82–118; T. Narazaki, Lp–Lq estimates for damped wave equations and their applications to semilinear problem, J. Math. Soc. Japan 56 (2004) 585–626]. And the blow-up is shown by the Fujita–Kaplan–Zhang method [Q. Zhang, A blow-up result for a nonlinear wave equation with damping: The critical case, C. R. Acad. Sci. Paris 333 (2001) 109–114; F. Sun, M. Wang, Existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping, Nonlinear Anal. 66 (12) (2007) 2889–2910; T. Ogawa, H. Takeda, Non-existence of weak solutions to nonlinear damped wave equations in exterior domains, Nonlinear Anal. 70 (10) (2009) 3696–3701]. 相似文献
16.
We establish a Stokes‐Fourier limit for the Boltzmann equation considered over any periodic spatial domain of dimension two or more. Appropriately scaled families of DiPerna‐Lions renormalized solutions are shown to have fluctuations that globally in time converge weakly to a unique limit governed by a solution of Stokes‐Fourier motion and heat equations provided that the fluid moments of their initial fluctuations converge to appropriate L2 initial data of the Stokes‐Fourier equations. Both the motion and heat equations are both recovered in the limit by controlling the fluxes and the local conservation defects of the DiPerna‐Lions solutions with dissipation rate estimates. The scaling of the fluctuations with respect to Knudsen number is essentially optimal. The assumptions on the collision kernel are little more than those required for the DiPerna‐Lions theory and that the viscosity and heat conduction are finite. For the acoustic limit, these techniques also remove restrictions to bounded collision kernels and improve the scaling of the fluctuations. Both weak limits become strong when the initial fluctuations converge entropically to appropriate L2 initial data. © 2001 John Wiley & Sons, Inc. 相似文献
17.
Norikazu Yamaguchi 《Mathematical Methods in the Applied Sciences》2005,28(13):1507-1526
In this paper we are concerned with the initial boundary value problem of the micropolar fluid system in a three dimensional bounded domain. We study the resolvent problem of the linearized equations and prove the generation of analytic semigroup and its time decay estimates. In particular, Lp–Lq type estimates are obtained. By use of the Lp–Lq estimates for the semigroup, we prove the existence theorem of global in time solution to the original nonlinear problem for small initial data. Furthermore, we study the magneto‐micropolar fluid system in the final section. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
18.
P. Penel 《Acta Appl Math》1994,37(1-2):137-145
We are concerned with the general case of compressible heat-conducting Navier-Stokes equations in three-dimensional exterior domains: It is shown that for small external data and both zero or nonzero velocity at infinity, there exists a unique (steady) solution inL
p-spaces,p > 3. We explain the approach and state the main results together with some a-priori estimates. 相似文献
19.
We prove extensions of our previous estimates for linear elliptic equations with inhomogeneous terms in L
p
spaces, p ≤ n to linear parabolic equations with inhomogeneous terms in L
p
, p ≤ n + 1. As with the elliptic case, our results depend on restrictions on parabolicity determined by certain subcones of the
positive cone . They also extend the maximum principle of Krylov for the case p = n + 1, corresponding to the usual parabolicity. 相似文献
20.
Joa Weber 《Mathematische Nachrichten》2013,286(1):88-104
Consider the linear parabolic partial differential equation ${\mathcal {D}}_u\xi =0$ which arises by linearizing the heat flow on the loop space of a Riemannian manifold M. The solutions are vector fields along infinite cylinders u in M. For these solutions we establish regularity and a priori estimates. We show that for nondegenerate asymptotic boundary conditions the solutions decay exponentially in L2 in forward and backward time. In this case ${\mathcal {D}}_u$ viewed as linear operator from the parabolic Sobolev space ${\mathcal {W}}^{1,p}$ to Lp is Fredholm whenever p > 1. We close with an Lp estimate for products of first order terms which is a crucial ingredient in the sequel 13 to prove regularity and the implicit function theorem. The results of the present text are the base to construct in 13 an algebraic chain complex whose homology represents the homology of the loop space. 相似文献