共查询到20条相似文献,搜索用时 15 毫秒
1.
DANCHIN Raphaёl 《中国科学 数学(英文版)》2012,55(2):245-275
Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations.In this survey paper,we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space.We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics. 相似文献
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利用解析性估计和方程非线性项的特殊结构,本文证明了三维各向异Navier-Stokes方程对一类在垂直方向慢变的大初值的整体适定性. 相似文献
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The purpose of this work is to solve the exterior Stokes problem in the half-space . We study the existence and the uniqueness of generalized solutions in weighted L
p
theory with 1 < p < ∞. Moreover, we consider the case of strong solutions and very weak solutions. This paper extends the studies done in Alliot,
Amrouche (Math. Methods Appl. 23:575–600, 2000) for an exterior Stokes problem in the whole space and in Amrouche, Bonzom
(Exterior Problems in the Half-space, submitted) for the Laplace equation in the same geometry as here.
相似文献
6.
We establish the energy equality for Leray–Hopf weak solutions of the 3D incompressible inhomogeneous Navier–Stokes equations in Lorentz–Besov spaces. This result may be regarded as an extension of that by Cheskidov and Luo (2020). 相似文献
7.
Sadek Gala 《Mathematical Methods in the Applied Sciences》2011,34(16):1945-1953
In this paper, we study the regularity criterion of weak solutions of the three dimensional micropolar fluid flows. It is proved that if the pressure satisfies where denotes the critical Besov space, then the weak solution (u,w) becomes a regular solution on (0,T]. This regularity criterion can be regarded as log in time improvements of the standard Serrin's criteria established before. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Sandrine Dubois 《Journal of Differential Equations》2003,189(1):99-147
We exhibit simple sufficient conditions which give weak-strong uniqueness for the 3D Navier-Stokes equations. The main tools are trilinear estimates and energy inequalities. We then apply our result to the framework of Lorentz, Morrey and Besov over Morrey spaces so as to get new weak-strong uniqueness classes and so uniqueness classes for solutions in the Leray-Hopf class. In the last section, we give a uniqueness and regularity result. We obtain new uniqueness classes for solutions in the Leray-Hopf class without energy inequalities but sufficiently regular. 相似文献
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This note studies the well‐posedness of the fractional Navier–Stokes equations in some supercritical Besov spaces as well as in the largest critical spaces for β ∈ (1/2,1). Meanwhile, the well‐posedness for fractional magnetohydrodynamics equations in these Besov spaces is also studied. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
11.
Bao-quan Yuan 《应用数学学报(英文版)》2010,26(3):381-386
With a Hǒlder type inequality in Besov spaces, we show that every strong solution θ(t, x) on (0, T ) of the dissipative quasi-geostrophic equations can be continued beyond T provided that ⊥θ(t, x) ∈L 2γ/γ-2δ ((0, T ); B^δ-γ/2 ∞∞(R^2)) for 0 〈 δ 〈 γ/2 . 相似文献
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The present work is dedicated to the well‐posedness issue of strong solutions (away from vacuum) to the compressible viscous magnetohydrodynamic (MHD) system in (d ≥ 2). We aim at extending those results in previous studies to more general Lp critical framework. Precisely, by recasting the whole system in Lagrangian coordinates, we prove the local existence and uniqueness of solutions by means of Banach fixed‐point theorem. Furthermore, with the aid of effective velocity, we employ the energy argument to establish global a priori estimates, which lead to the unique global solution near constant equilibrium. Our results hold in case of small data but large highly oscillating initial velocity and magnetic field. 相似文献
14.
Cheng He 《数学学报(英文版)》1999,15(2):153-164
By making full use of the estimates of solutions to nonstationary Stokes equations and the method discussing global stability,
we establish the global existence theorem of strong solutions for Navier-Stokes equatios in arbitrary three dimensional domain
with uniformlyC
3 boundary, under the assumption that |a|
L
2(Θ) + |f|
L
1(0,∞;L
2(Θ)) or |∇a|
L
2(Θ) + |f|
L
2(0,∞;L
2(Θ)) small or viscosityv large. Herea is a given initial velocity andf is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary
conditions is also discussed.
This work is supported by foundation of Institute of Mathematics, Academia Sinica 相似文献
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The regularity criterion of the weak solution to the 3D viscous Boussinesq equations in Besov spaces
Zhaoyin Xiang 《Mathematical Methods in the Applied Sciences》2011,34(3):360-372
In this paper, by using the Fourier localization technique and Bony's paraproduct decomposition, we give a regularity criterion of the weak solution to 3D viscous Boussinesq equations in Besov spaces. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Kuijie Li Baoxiang Wang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(6):1679-1707
This paper is concerned with the blowup criterion for mild solution to the incompressible Navier–Stokes equation in higher spatial dimensions . By establishing an ? regularity criterion in the spirit of [11], we show that if the mild solution u with initial data in , becomes singular at a finite time , then The corresponding result in 3D case has been obtained in [24]. As a by-product, we also prove a regularity criterion for the Leray–Hopf solution in the critical Besov space, which generalizes the results in [17], where blowup criterion in critical Lebesgue space is addressed. 相似文献
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The time-periodic Stokes problem in a half-space with fully inhomogeneous right-hand side is investigated. Maximal regularity in a time-periodic Lp setting is established. A method based on Fourier multipliers is employed that leads to a decomposition of the solution into a steady-state and a purely oscillatory part in order to identify the suitable function spaces. 相似文献
20.
Guilong Gui 《Journal of Functional Analysis》2011,261(11):3181-3210
Motivated by Chemin and Gallagher (2010) [8], we consider the global wellposedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with large initial velocity slowly varying in one space variable. In particular, we proved that when the initial density is close enough to a positive constant, then given divergence free initial velocity field of the type , as that in Chemin and Gallagher (2010) [8] for the classical Navier-Stokes system, we shall prove the global wellposedness of (INS) for ? sufficiently small. The main difficulty here lies in the fact that we will have to obtain the L1(R+;Lip(R3)) estimate for convection velocity in the transport equation of (INS). Toward this and due to the strong anisotropic properties of the approximate solutions, we will have to work in the framework of anisotropic type Besov spaces here. 相似文献