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作者:A. Shnirelman
来源:[J].Communications in Mathematical Physics(IF 1.971), 2000, Vol.210 (3), pp.541-603Springer
摘要:Abstract:(#br) Weak solution of the Euler equations is an L 2 -vector field u ( x , t ), satisfying certain integral relations, which express incompressibility and the momentum balance. Our conjecture is that some weak solutions are limits of solutions of viscous and compressible...
作者:A. Shnirelman
来源:[J].Handbook of Mathematical Fluid Dynamics, 2003, Vol.2, pp.87-116Elsevier
摘要:Abstract(#br)A weak solution of the Euler equations is an L 2 -vector field u(x.t), satisfying certain integral relations, which express ineompressibility and the momentum balance. Our conjecture is that some weak solutions are limits of solutions of viscous and compressible flui...
作者:A. Shnirelman
来源:[J].American Journal of Mathematics(IF 1.35), 1997, Vol.119 (3), pp.579-608JSTOR
摘要:The Liapunov Function is a continuous function, defined in the phase space of a dynamical system, which grows along every trajectory. Its existence means certain irreversibility of the system. Generalized Liapunov Function is a continuous function with values in some topological ...
作者:A. Shnirelman
来源:[J].Journal of Mathematical Sciences, 2005, Vol.128 (2), pp.2818-2821Springer
摘要:Abstract(#br)The motion of an ideal incompressible fluid in a two-dimensional domain M is considered. We assume that the initial velocity field is small-scaled, i.e., its Fourier transform is concentrated at high frequences. The extreme case of flows corresponding to solutions of...
作者:A. Shnirelman
来源:[J].Global and Stochastic Analysis, 2015, Vol.2 (2)Mind Reader Publications
摘要:A new proof is given of the fact that the particle trajec- tories of the ideal incompressible °uid are analytic curves, though the solutions of the Euler equations may have a ¯nite regularity. This is a consequence of a general fact that the geodesic exponential map on the g...
作者:A. Shnirelman
来源:[B].Elsevier Inc.2003Elsevier
摘要:Abstract A weak solution of the Euler equations is an L 2 -vector field u(x.t), satisfying certain integral relations, which express ineompressibility and the momentum balance. Our conjecture is that some weak solutions are limits of solutions of viscous and compressible fluid eq...
作者:A. Shnirelman
来源:[J].2005, Vol.128 (2), pp.2818-2821IntechOpen
作者:A. Shnirelman
来源:[J].American Journal of Mathematics(IF 1.35), 1997, Vol.119 (3), pp.579-608ZBMATH
摘要:The aim of this paper is to construct a generalized Lyapunov function and a generalized integral for an ideal incompressibe fluid, namely the case of a fluid moving on a standard 2-dimensional torus $\bbfT^2$. \par The configuration space ${\cal D}B_s$ consists of all diffeomorph...

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