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51.
The aim of this note is to generalize and apply results on matrix continued fractions representing the solution of discrete matrix Riccati equations. Assuming uniform bounds for the norm of the matrix coefficients of the continued fraction, the minimal and maximal solutions of the corresponding algebraic Riccati equation can be accurately enclosed. 相似文献
52.
David Hoff 《Journal of Mathematical Fluid Mechanics》2005,7(3):315-338
We prove the global existence of weak solutions of the Navier–Stokes equations of compressible flow in a half-space with the boundary condition proposed by Navier: the velocity on the boundary is proportional to the tangential component of the stress. This boundary condition allows for the determination of the scalar function in the Helmholtz decomposition of the acceleration density, which in turn is crucial in obtaining pointwise bounds for the density. Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. These results generalize previous results for solutions in the whole space and are the first for solutions in this intermediate regularity class in a region with a boundary. 相似文献
53.
Michael Bildhauer 《manuscripta mathematica》1998,97(3):389-406
H?lder continuity up to the free boundary is proved for minimizing solutions if they meet the supporting surface in an angle
which is bounded away from zero. The problem is localized by proving the continuity of the distance function, a result which
is also true for stationary points.
Received: 14 April 1998 相似文献
54.
Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism. 相似文献
55.
This paper studies the pullback asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid in two-dimensional (2D) bounded domains. We first prove the existence of pullback attractors AV in space V (has H2-regularity, see notation in Section 2) and AH in space H (has L2-regularity) for the cocycle corresponding to the solutions of the fluid. Then we verify the regularity of the pullback attractors by showing AV=AH, which implies the pullback asymptotic smoothing effect of the fluid in the sense that the solutions become eventually more regular than the initial data. 相似文献
56.
Rupert L. Frank Ari Laptev Elliott H. Lieb Robert Seiringer 《Letters in Mathematical Physics》2006,77(3):309-316
Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential. 相似文献
57.
Jun Hu Zhong-Ci Shi 《计算数学(英文版)》2006,24(1):1-8
We consider the quadrilateral Q1 isoparametric element and establish an optimal error estimate in H^1 norm for the interpolation operator under a weaker mesh condition which admits anisotropic quadrilaterals and allows the quadrilateral to become a regular triangle in the sense of maximum angle condition [5, 11]. 相似文献
58.
All the symmetries and conservation laws of Navier-Stokes equations are calculated. 相似文献
59.
The first object of this paper is to introduce a new evolution equation for the characteristic function of the boundary Γ
of a Lipschitzian domain Ω in the N-dimensional Euclidean space under the influence of a smooth time-dependent velocity field. The originality of this equation is that the evolution takes place in an Lp-space with respect to the (N − 1)-Hausdorff measure. A second more speculative objective is to discuss how that equation can be relaxed to rougher velocity
fields via some weak formulation. A candidate is presented and some of the technical difficulties and open issues are discussed.
Continuity results in several metric topologies are also presented. The paper also specializes the results on the evolution
of the oriented distance function to initial sets with zero N-dimensional Lebesgue measure. 相似文献
60.
Armen Shirikyan 《Probability Theory and Related Fields》2006,134(2):215-247
We consider a class of dissipative PDE's perturbed by an external random force. Under the condition that the distribution
of perturbation is sufficiently non-degenerate, a strong law of large numbers (SLLN) and a central limit theorem (CLT) for
solutions are established and the corresponding rates of convergence are estimated. It is also shown that the estimates obtained
are close to being optimal. The proofs are based on the property of exponential mixing for the problem in question and some
abstract SLLN and CLT for mixing-type Markov processes. 相似文献