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Preprint
On the convergence of trajectory statistical solutions
02 Dec 2024
Abstract
In this work, a recently introduced general framework for trajectory
statistical solutions is considered, and the question of convergence of
families of such solutions is addressed. Conditions for the convergence are
given which rely on natural assumptions related to a priori estimates for the
individual solutions of typical approximating problems. The first main result
is based on the assumption that the superior limit of suitable families of
compact subsets of carriers of the family of trajectory statistical solutions
be included in the set of solutions of the limit problem. The second main
result is a version of the former in the case in which the approximating family
is associated with a well-posed system. These two results are then applied to
the inviscid limit of incompressible Navier-Stokes system in two and three
spatial dimensions, showing, in particular, the existence of trajectory
statistical solutions to the two- and three-dimensional Euler equations, in the
context of weak and dissipative solutions, respectively. Another application of
the second main result is on the Galerkin approximations of statistical
solutions of the three-dimensional Navier-Stokes equations.
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Details
- Title
- On the convergence of trajectory statistical solutions
- Creators
- Anne C BronziCecilia F MondainiRicardo M. S Rosa
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021970101304721