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摘要
We show that continuous dependence on initial data of solutions to the Euler equations of incompressible hydrodynamics is optimal. More precisely, we prove that the data-to-solution map is not uniformly continuous in Sobolev H(s)(Omega) topology for any s is an element of R if the domain Omega is the (flat) torus T(n) = R(n)/2 pi Z(n) and for any s > 0 if the domain is the whole space R(n).
- 出版日期2010-5
