共查询到20条相似文献,搜索用时 15 毫秒
1.
We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative anti-symmetric perturbation of 2D incompressible Euler equations and generalized fractional dissipative 2D Boussinesq equations. 相似文献
2.
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
3.
4.
张志军 《数学物理学报(B辑英文版)》2008,28(3):595-603
By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem Δu = k(x)g(u), u 〉 0, x ∈ Ω, u|δΩ =+∞, where Ω is a bounded domain with smooth boundary in R^N; g ∈ C^1[0, ∞), g(0) = g'(0) = 0, and there exists p 〉 1, such that lim g(sξ)/g(s)=ξ^p, ↓Aξ 〉 0, and k ∈ Cloc^α(Ω) is non-negative non-trivial in D which may be singular on the boundary. 相似文献
5.
Dipendra Regmi & Jiahong Wu 《数学研究》2016,49(2):169-194
This paper studies the global existence and regularity of classical solutions
to the 2D incompressible magneto-micropolar equations with partial dissipation. The
magneto-micropolar equations model the motion of electrically conducting micropolar
fluids in the presence of a magnetic field. When there is only partial dissipation, the
global regularity problem can be quite difficult. We are able to single out three special
partial dissipation cases and establish the global regularity for each case. As special
consequences, the 2D Navier-Stokes equations, the 2D magnetohydrodynamic equations,
and the 2D micropolar equations with several types of partial dissipation always
possess global classical solutions. The proofs of our main results rely on anisotropic
Sobolev type inequalities and suitable combination and cancellation of terms. 相似文献
6.
In this article we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampère equations, recently established by De Philippis and Figalli [14], to provide global in time existence of distributional solutions to the semigeostrophic equations on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed. 相似文献
7.
The aim of the paper is to develop the Fourier Analysis techniques needed in the study of optimal well-posedness and global regularity properties of the Yang-Mills equations in Minkowski space-time , for the case of the critical dimension . We introduce new functional spaces and prove new bilinear estimates for solutions of the homogeneous wave equation, which can be viewed as generalizations of the well-known Strichartz-Pecher inequalities.
8.
This paper is dedicated to establishing the global regularity for the two dimensional magnetohydrodynamic equations with fractional anisotropic dissipation when the fractional powers are restricted to some certain ranges. In addition, the global regularity results for the two dimensional magnetohydrodynamic equations with partial dissipation are also obtained. Consequently, these results bring us more closer to the resolution of the global regularity problem on the two dimensional magnetohydrodynamic equations with standard Laplacian magnetic diffusion. 相似文献
9.
10.
R. Croisot in 1953, stated a very interesting problem of classification of
all types of the regularity of semigroups defined by equations of the form
a = amxan, with m,n \ge 0, m + n \ge 2. He proved that any of these equations
determines either the ordinary regularity, left, right or complete regularity
(see also the book by A. H. Clifford and G. B. Preston, Section 4.1). A
similar problem, concerning all types of the regularity of semigroups and their
elements defined by equations of the form a = apxaqyar, with p,q,r \ge 0,
was treated by S. Lajos and G. Szász in 1975. The purpose of this paper
is to generalize the results by Croisot, Lajos and Szász considering all
types of the regularity of semigroups and their elements determined by more
general equations called linear. We determine all types of the regularity of
elements defined by linear equations, and prove that there are exactly 14 types
of the regularity of semigroups defined by such equations. We also give
implication diagrams for linear equations and regularity conditions. 相似文献
11.
For the 3D incompressible Hall magneto-hydrodynamics equations, global regularity of the weak solutions is not established so far. The major difficulty is that the dissipation given by the Laplacian operator is insufficient to control the nonlinearities. Wan obtained the global regularities of the 3D generalized Hall-MHD equations with critical and subcritical hyperdissipation in ({\em Global regularity for generalized Hall-magnetohydrodynamics systems}, Electron. J. Differential Equations, 2015, 2015(179), 1--18). We improve this slightly by making logarithmic reductions in the dissipation and still obtain the global regularity. 相似文献
12.
In this paper we are concerned with the maximum principle for quasi-linear backward stochastic partial differential equations (BSPDEs for short) of parabolic type. We first prove the existence and uniqueness of the weak solution to quasi-linear BSPDEs with the null Dirichlet condition on the lateral boundary. Then using the De Giorgi iteration scheme, we establish the maximum estimates and the global maximum principle for quasi-linear BSPDEs. To study the local regularity of weak solutions, we also prove a local maximum principle for the backward stochastic parabolic De Giorgi class. 相似文献
13.
The non blow-up of the 3D ideal incompressible magnetohydrodynamics (MHD) equations is proved for a class of three-dimensional
initial data characterized by uniformly large vorticity and magnetic field in bounded cylindrical domains. There are no conditional
assumptions on properties of solutions at later times, nor are the global solutions close to some 2D manifold. The approach
of proving regularity is based on investigation of fast, singular, oscillating limits and nonlinear averaging methods in the
context of almost periodic functions. We establish the global regularity of the 3D limit resonant MHD equations without any
restrictions on the size of the 3D initial data. After establishing the strong convergence to the limit resonant equations,
we bootstrap this into the regularity on arbitrarily large time intervals for solutions of the 3D MHD equations with weakly-aligned
uniformly large vorticity and magnetic field at t = 0. Bibliography: 36 titles.
Dedicated to the memory of O. A. Ladyzhenskaya
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 203–219. 相似文献
14.
Whether or not classical solutions of the 2D incompressible MHD equations without full dissipation and magnetic diffusion can develop finite-time singularities is a difficult issue. A major result of this paper establishes the global regularity of classical solutions for the MHD equations with mixed partial dissipation and magnetic diffusion. In addition, the global existence, conditional regularity and uniqueness of a weak solution is obtained for the 2D MHD equations with only magnetic diffusion. 相似文献
15.
Global Regularity of the Logarithmically Supercritical MHD System in Two-dimensional Space 下载免费PDF全文
Min Cheng 《Journal of Nonlinear Modeling and Analysis》2020,2(4):573-584
In this paper, we study the global regularity of logarithmically supercritical MHD equations in $2$ dimensional, in which the dissipation terms are $-\mu\Lambda^{2\alpha}u$ and $-\nu\mathcal{L}^{2\beta} b$. We show that global regular solutions in the cases $0<\alpha<\frac{1}{2},\beta>1,3\alpha+2\beta>3$. 相似文献
16.
Xing Ruixiang Pan Hongjing 《偏微分方程(英文版)》2008,21(3):221-233
In this paper, we derive a priori bounds for global solutions of 2m-th order semilinear parabolic equations with superlinear and subcritical growth conditions. The proof is obtained by a bootstrap argument and maximal regularity estimates. If n≥ 10/3m, we also give another proof which does not use maximal regularity estimates. 相似文献
17.
This paper is devoted to the global in time existence of classical solutions to the d-Dimensional (dD) micropolar equations with fractional dissipation. Micropolar equations model a class of fluids with nonsymmetric stress tensor such as fluids consisting of particles suspended in a viscous medium. It remains unknown whether or not smooth solutions of the classical 3D micropolar equations can develop finite-time singularities. The purpose here is to explore the global regularity of solutions for dD micropolar equations under the smallest amount of dissipation. We establish the global regularity for two important fractional dissipation cases. Direct energy estimates are not sufficient to obtain the desired global a priori bounds in each case. To overcome the difficulties, we employ the Besov space techniques. 相似文献
18.
Pierre Dreyfuss 《Potential Analysis》2007,26(2):101-119
We prove that under some global conditions on the maximum and the minimum eigenvalue of the matrix of the coefficients, the gradient of the (weak) solution of some degenerate elliptic equations has higher integrability than expected. Technically we adapt the Giaquinta–Modica regularity method in some degenerate cases. When the dimension is two, a consequence of our result is a new Hölder continuity result for the weak solution. 相似文献
19.
Dipendra Regmi 《Mathematical Methods in the Applied Sciences》2019,42(12):4305-4317
We study the global existence and regularity of classical solutions to the 2D incompressible magneto‐micropolar equations with partial dissipation. We establish the global regularity for one partial dissipation case. The proofs of our main results rely on anisotropic Sobolev type inequalities and suitable combination and cancellation of terms. 相似文献
20.
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