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151.
We consider a generalization of Camassa–Holm‐type equation including the Camassa–Holm equation and the Novikov equation. We mainly establish the existence of solutions in lower order Sobolev space with . Then, we present a precise blowup scenario and give a global existence result of strong solutions. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
152.
The authors construct a solution Ut(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity, namely one-fold differentiability. Besides, the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained. 相似文献
153.
The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds. 相似文献
154.
We consider the n-dimensional modified quasi-geostrophic (SQG) equations
with κ > 0, α ∈ (0,1] and θ0 ∈ W1, ∞ (?n). In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu [5], who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case. The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol [2]. 相似文献
t∂θ + u . ∇θ + κΛαθ = 0,
u = Λα-1 R⊥θ
155.
《Applied Mathematical Modelling》2014,38(9-10):2601-2612
This study devotes to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for unconstrained optimization. The primary objective of the paper is to introduce a more relaxed trust-region approach based on a novel extension in trust-region ratio and radius. The next aim is to employ stronger nonmonotone strategies, i.e. bigger trust-region ratios, far from the optimizer and weaker nonmonotone strategies, i.e. smaller trust-region ratios, close to the optimizer. The global convergence to first-order stationary points as well as the local superlinear and quadratic convergence rates are also proved under some reasonable conditions. Some preliminary numerical results and comparisons are also reported. 相似文献
156.
In this paper, we are concerned with the partial regularity for suitable weak solutions of the tri-dimensional magnetohydrodynamic equations. With the help of the De Giorgi iteration method, we obtain the results proved by He and Xin (C. He, Z. Xin, Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations, J. Funct. Anal. 227 (2005) 113–152), namely, the one dimensional parabolic Hausdorff measure of the possible singular points of the velocity field and the magnetic field is zero. 相似文献
157.
We study the numerical radius of Lipschitz operators on Banach spaces via the Lipschitz numerical index, which is an analogue of the numerical index in Banach space theory. We give a characterization of the numerical radius and obtain a necessary and sufficient condition for Banach spaces to have Lipschitz numerical index 1. As an application, we show that real lush spaces and C -rich subspaces have Lipschitz numerical index 1. Moreover, using the Gâteaux differentiability of Lipschitz operators, we characterize the Lipschitz numerical index of separable Banach spaces with the RNP. Finally, we prove that the Lipschitz numerical index has the stability properties for the c0-, l1-, and l∞-sums of spaces and vector-valued function spaces. From this, we show that the C(K) spaces, L1(μ)-spaces and L∞(ν)-spaces have Lipschitz numerical index 1. 相似文献
158.
159.
160.
We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, which we provide. 相似文献