Home About us Contact
|
Home About us Contact | ||
|
|
||
Dimension N (dimension + n)
Selected AbstractsFour-dimensional variational assimilation in the unstable subspace and the optimal subspace dimensionTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 647 2010Anna Trevisan Abstract Key apriori information used in 4D-Var is the knowledge of the system's evolution equations. In this article we propose a method for taking full advantage of the knowledge of the system's dynamical instabilities in order to improve the quality of the analysis. We present an algorithm for four-dimensional variational assimilation in the unstable subspace (4D-Var , AUS), which consists of confining in this subspace the increment of the control variable. The existence of an optimal subspace dimension for this confinement is hypothesized. Theoretical arguments in favour of the present approach are supported by numerical experiments in a simple perfect nonlinear model scenario. It is found that the RMS analysis error is a function of the dimension N of the subspace where the analysis is confined and is a minimum for N approximately equal to the dimension of the unstable and neutral manifold. For all assimilation windows, from 1 to 5 d, 4D-Var , AUS performs better than standard 4D-Var. In the presence of observational noise, the 4D-Var solution, while being closer to the observations, is farther away from the truth. The implementation of 4D-Var , AUS does not require the adjoint integration. Copyright © 2010 Royal Meteorological Society [source] On the well-posedness of the Cauchy problem for an MHD system in Besov spacesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2009Changxing Miao Abstract This paper is devoted to the study of the Cauchy problem of incompressible magneto-hydrodynamics system in the framework of Besov spaces. In the case of spatial dimension n,3, we establish the global well-posedness of the Cauchy problem of an incompressible magneto-hydrodynamics system for small data and the local one for large data in the Besov space , (,n), 1,p<, and 1,r,,. Meanwhile, we also prove the weak,strong uniqueness of solutions with data in , (,n),L2(,n) for n/2p+2/r>1. In the case of n=2, we establish the global well-posedness of solutions for large initial data in homogeneous Besov space , (,2) for 2 Bodies of constant width in arbitrary dimensionMATHEMATISCHE NACHRICHTEN, Issue 7 2007Thomas Lachand-Robert Abstract We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n , 1)-dimensional projection being given. We give a number of examples, like a four-dimensional body of constant width whose 3D-projection is the classical Meissner's body. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Density results relative to the Dirichlet energy of mappings into a manifoldCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2006Mariano Giaquinta Let ,, be a smooth, compact, oriented Riemannian manifold without boundary. Weak limits of graphs of smooth maps uk:Bn , ,, with an equibounded Dirichlet integral give rise to elements of the space cart2,1 (Bn × ,,). Assume that ,, is 1-connected and that its 2-homology group has no torsion. In any dimension n we prove that every element T in cart2,1 (Bn × ,,) with no singular vertical part can be approximated weakly in the sense of currents by a sequence of graphs of smooth maps uk:Bn , ,, with Dirichlet energies converging to the energy of T. © 2006 Wiley Periodicals, Inc. [source] Regularity of minimizers of semilinear elliptic problems up to dimension 4COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 10 2010Xavier Cabré We consider the class of semistable solutions to semilinear equations ,,u = f(u) in a bounded smooth domain , of \input amssym $\Bbb R^n$ (with , convex in some results). This class includes all local minimizers, minimal, and extremal solutions. In dimensions n , 4, we establish an a priori L, -bound that holds for every positive semistable solution and every nonlinearity f. This estimate leads to the boundedness of all extremal solutions when n = 4 and , is convex. This result was previously known only in dimensions n , 3 by a result of G. Nedev. In dimensions 5 , n , 9 the boundedness of all extremal solutions remains an open question. It is only known to hold in the radial case , = BR by a result of A. Capella and the author. © 2010 Wiley Periodicals, Inc. [source]
| | |||||||||