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Transport-Elliptic Estimates

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0027
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter solves the underdetermined, elliptic equation ∂ⱼQsuperscript jl = Usuperscript l and Qsuperscript jl = Qsuperscript lj (Equation 1069) in order to eliminate the error term in the ... More


The Coarse Scale Flow and Commutator Estimates

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0016
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter derives estimates for the coarse scale flow and commutator. Instead of mollifying the velocity field in the time variable, it derives a Transport equation for vsubscript Element and some ... More


Transport Estimates

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0017
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter derives estimates for quantities which are transported by the coarse scale flow and for their derivatives. It first considers the phase functions which satisfy the Transport equation, ... More


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