摘要:

AbstractIt is shown that for an appropriate class of dissipatively perturbed Hamiltonian systems, the number of unstable modes of the dynamics linearized at a nondegenerate equilibrium is determined solely by the index of the equilibrium regarded as a critical point of the Hamiltonian. In addition, the movement of the associated eigenvalues in the limit of vanishing dissipation is analyzed. ©1995 John Wiley&Sons, Inc

ISSN:0010-3640    

DOI:10.1002/cpa.3160480602

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

摘要:

AbstractWe prove the convergence of vortex blob methods to classical weak solutions for the two‐dimensional incompressible Euler equations with initial data satisfying the conditions that the vorticity is a finite Radon measure of distinguished sign and the kinetic energy is locally bounded. This includes the important example of vortex sheets. The result is valid as long as the computational grid sizehdoes not exceed the smoothing blob size ε, i.e.,h/ε ≦C.. ©1995 John Wiley&Son

ISSN:0010-3640    

DOI:10.1002/cpa.3160480603

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

摘要:

AbstractA scale of Banach spaces is considered as a single weighted Banach space. A variant of the Cauchy‐Kovalevskaya theorem is proved, including the results of Nirenberg and Nishida for the abstract nonlinear Cauchy problem. ©1995 John Wiley&Sons, I

ISSN:0010-3640    

DOI:10.1002/cpa.3160480604

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160480605

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

摘要:

AbstractWe seek metrics conformal to the standard ones onSnhaving prescribed Gaussian curvature in casen= 2 (the Nirenberg Problem), or prescribed scalar curvature forn≧ 3 (the Kazdan‐Warner problem). There are well‐known Kazdan‐Warner and Bourguignon‐Ezin necessary conditions for a functionR(x)to be the scalar curvature of some conformally related metric. Are those necessary conditions also sufficient? This problem has been open for many years.In a previous paper, we answered the question negatively by providing a family of counter examples.In this paper, we obtain much stronger results. We show that, in all dimensions, ifR(x)is rotationally symmetric and monotone in the region where it is positive, then the problem has no solution at all. It follows that, onS2, for a non‐degenerate, rotationally symmetric functionR(θ), a necessary and sufficient condition for the problem to have a solution is thatRθ changes signs in the region where it is positive. This condition, however, is still not sufficient to guarantee the existence of a rotationally symmetric solution, as will be shown in this paper. We also consider similar necessary conditions for non‐symmetric functions. ©1995 John

ISSN:0010-3640    

DOI:10.1002/cpa.3160480606

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160480601

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY