On the number of determining nodes for the 2D Navier-Stokes equations

Don A. Jones; Edriss S. Titi

doi:10.1016/0022-247X(92)90190-O

On the number of determining nodes for the 2D Navier-Stokes equations

Don A. Jones, Edriss S. Titi

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

It is known that the solutions of the 2D Navier-Stokes equations, in bounded domains, are determined by a finite discrete set of nodal values. That is if the large time behavior of the solutions to the Navier-Stokes equations is known on an appropriate finite discrete set, then the large time behavior of the solution itself is totally determined. Here, an upper-bound is rigorously established for the number of nodes needed to determine the solutions of the Navier-Stokes equations in two dimensions with periodic boundary conditions.

Original language	English (US)
Pages (from-to)	72-88
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	168
Issue number	1
DOIs	https://doi.org/10.1016/0022-247X(92)90190-O
State	Published - Jul 15 1992
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/0022-247X(92)90190-O

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title = "On the number of determining nodes for the 2D Navier-Stokes equations",

abstract = "It is known that the solutions of the 2D Navier-Stokes equations, in bounded domains, are determined by a finite discrete set of nodal values. That is if the large time behavior of the solutions to the Navier-Stokes equations is known on an appropriate finite discrete set, then the large time behavior of the solution itself is totally determined. Here, an upper-bound is rigorously established for the number of nodes needed to determine the solutions of the Navier-Stokes equations in two dimensions with periodic boundary conditions.",

author = "Jones, {Don A.} and Titi, {Edriss S.}",

note = "Funding Information: It is our pleasuret o thank Professor Ciprian Foias for the stimulatinga nd interesting discussions.P art of this work was done when D.A.J. enjoyed the hospitality of Indiana University.T he work of EST. was partly supportedb y AFOSR, NSF Grant DMS-8915672, and the U. S. Army ResearchO fficet hrought he MSI, Cornell University.",

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doi = "10.1016/0022-247X(92)90190-O",

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AU - Titi, Edriss S.

N1 - Funding Information: It is our pleasuret o thank Professor Ciprian Foias for the stimulatinga nd interesting discussions.P art of this work was done when D.A.J. enjoyed the hospitality of Indiana University.T he work of EST. was partly supportedb y AFOSR, NSF Grant DMS-8915672, and the U. S. Army ResearchO fficet hrought he MSI, Cornell University.

PY - 1992/7/15

Y1 - 1992/7/15

N2 - It is known that the solutions of the 2D Navier-Stokes equations, in bounded domains, are determined by a finite discrete set of nodal values. That is if the large time behavior of the solutions to the Navier-Stokes equations is known on an appropriate finite discrete set, then the large time behavior of the solution itself is totally determined. Here, an upper-bound is rigorously established for the number of nodes needed to determine the solutions of the Navier-Stokes equations in two dimensions with periodic boundary conditions.

AB - It is known that the solutions of the 2D Navier-Stokes equations, in bounded domains, are determined by a finite discrete set of nodal values. That is if the large time behavior of the solutions to the Navier-Stokes equations is known on an appropriate finite discrete set, then the large time behavior of the solution itself is totally determined. Here, an upper-bound is rigorously established for the number of nodes needed to determine the solutions of the Navier-Stokes equations in two dimensions with periodic boundary conditions.

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On the number of determining nodes for the 2D Navier-Stokes equations

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