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91.
Yuan Jia 《偏微分方程(英文版)》2008,21(3):208-220
We give blow-up criteria of strong solutions of Navier-Stokes equations with its initial data in Besov spaces and consider the regularity of Leray-Hopf solutions of the equation. 相似文献
92.
关于分层空间度量化的一个问题 总被引:1,自引:0,他引:1
利用g-函数研究广义度量空间和度量化,统一了近年来许多有趣的工作.本文回答了[2]中提出的一个问题.所讨论的拓扑空间是正则的. 相似文献
93.
We establish sharp estimates for some multilinear commutators related to the Littlewood-Paley and Marcinkiewicz operators.
As an application, we obtain the weighted norm inequalities and L log L type estimate for the multilinear commutators.
相似文献
94.
Let T be a product Calderón-Zygmund singular integral introduced by Journé. Using an elegant rectangle atomic decomposition of Hp(Rn×Rm) and Journé's geometric covering lemma, R. Fefferman proved the remarkable Hp(Rn×Rm)−Lp(Rn×Rm) boundedness of T. In this paper we apply vector-valued singular integral, Calderón's identity, Littlewood-Paley theory and the almost orthogonality together with Fefferman's rectangle atomic decomposition and Journé's covering lemma to show that T is bounded on product Hp(Rn×Rm) for if and only if , where ε is the regularity exponent of the kernel of T. 相似文献
95.
证明一类带粗糙核平方函数的加权及l~r-向量值不等式,其中所用的权函数为径向权.作为推论,我们得出了带H~1-核的Marcinkiewicz积分μ_Ω的相应不等式. 相似文献
96.
In this paper, we study the well-posedness of the thermal boundary layer equation in two-dimensional incompressible heat conducting flow. The thermal boundary layer equation describes the behavior of thermal layer and viscous layer for the two-dimensional incompressible viscous flow with heat conduction in the small viscosity and heat conductivity limit. When the initial datum are analytic, with respect to the tangential variable of the boundary, and without the monotonicity condition of the tangential velocity, by using the Littlewood-Paley theory, we obtain the local-in-time existence and uniqueness of solution to this thermal boundary layer problem. 相似文献
97.
Given initial data u0 ∈ Lp(R3) for some p in[3, 18/5[, the auhtors ?rst prove that 3D incompressible Navier-Stokes system has a unique solution u = uL+v with uL def = et?u0 and v ∈ e L∞([0, T]; ˙ H5/2 ? 6/p ) ∩ L1(]0, T[; ˙H9/2 ? 6/p ) for some positive time T. Then they derive an explicit lower bound for the radius of space analyticity of v, which in particular extends the corresponding results in [Chemin, J.-Y., Gallagher, I. and Zhang, P., On the radius of analyticity of solutions to semi-linear parabolic system, Math. Res. Lett., 27, 2020, 1631– 1643, Herbst, I. and Skibsted, E., Analyticity estimates for the Navier-Stokes equations, Adv. in Math., 228, 2011, 1990–2033] with initial data in ˙Hs(R3) for s∈[1/2,3/2[. 相似文献
98.
Endpoint estimates of generalized homogeneous Littlewood–Paley <Emphasis Type="Italic">g</Emphasis>-functions over non-homogeneous metric measure spaces 下载免费PDF全文
Let (χ, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. Under the weak reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-functionr (r∈[2,∞)) is bounded from Hardy space H1(μ) into L1(μ). Moreover, the authors show that, if f ∈ RBMO(μ), then[r(f)]r is either infinite everywhere or finite almost everywhere, and in the latter case,[r(f)]r belongs to RBLO(μ) with the norm no more than ‖f‖RBMO(μ) multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness ofr from RBMO(μ) into RBLO(μ). The vector valued Calderón-Zygmund theory over (χ, d, μ) is also established with details in this paper. 相似文献
99.
Let hR denote an L∞ normalized Haar function adapted to a dyadic rectangle R⊂d[0,1]. We show that for choices of coefficients α(R), we have the following lower bound on the L∞ norms of the sums of such functions, where the sum is over rectangles of a fixed volume:
100.
Ryo Takada 《Journal of Evolution Equations》2008,8(4):693-725
We introduce Besov type function spaces, based on the weak L
p
-spaces instead of the standard L
p
-spaces, and prove a local-in-time unique existence and a blow-up criterion of solutions in those spaces for the Euler equations
of perfect incompressible fluid in . For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator type estimates in our weak spaces.
Abbreviate title: Euler equations in Besov spaces of weak type 相似文献