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Type: Artigo de periódico
Title: Abstract Framework For The Theory Of Statistical Solutions
Abstract: An abstract framework for the theory of statistical solutions is developed for general evolution equations, extending the theory initially developed for the three-dimensional incompressible Navier-Stokes equations. The motivation for this concept is to model the evolution of uncertainties on the initial conditions for systems which have global solutions that are not known to be unique. Both concepts of statistical solution in trajectory space and in phase space are given, and the corresponding results of existence of statistical solution for the associated initial value problems are proved. The wide applicability of the theory is illustrated with the very incompressible Navier-Stokes equations, a reaction-diffusion equation, and a nonlinear wave equation, all displaying the property of global existence of weak solutions without a known result of global uniqueness. © 2016 Elsevier Inc.
Editor: Academic Press Inc.
Rights: fechado
Identifier DOI: 10.1016/j.jde.2016.02.027
Date Issue: 2016
Appears in Collections:Unicamp - Artigos e Outros Documentos

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