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On some regularity problems in the t...

Jia, Hao.

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On some regularity problems in the theory of Navier Stokes equation.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On some regularity problems in the theory of Navier Stokes equation./
Author:	Jia, Hao.
Description:	73 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.
Contained By:	Dissertation Abstracts International74-11B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3589053
ISBN:	9781303275241

On some regularity problems in the theory of Navier Stokes equation.
Jia, Hao.

On some regularity problems in the theory of Navier Stokes equation. - 73 p.

Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.

Thesis (Ph.D.)--University of Minnesota, 2013.

We present some results obtained jointly with Professor Vladimir Sverak, in the study of some problems in the regularity theory of Navier Stokes equations, and some Liouville theorems for time-dependent Stokes system in domains jointly with Professor Vladimir Sverak and Gregory Seregin. In the first part of the thesis, we prove that the regularity of weak solution (called Leray solution) depends only locally on the regularity properties of the initial data, at least for a short time. This observation is then used to prove existence of scale-invariant solutions to the Navier Stokes equation with --1- homogeneous initial data without smallness condition. The main point of the result is that it seems to be out of reach of perturbation methods, and it provides valuable insights into the possible non-uniqueness of Leray-Hopf solutions, which is a long standing open problem in this area. In the second part of the thesis, we give a simple proof of the existence of initial data with minimal L3-norm for potential Navier-Stokes singularities, recently established in "Gallagher, I., Koch, G.S., Planchon, F., A profile decomposition approach to the Linfinityt&parl0;L3x &parr0; Navier-Stokes regularity criterion, Math. Ann. (published online July 2012)" with techniques based on profile decomposition. Our proof is more elementary, and is based on suitable splittings of initial data and energy methods. The main difficulty in the L3 case is the lack of compactness of the imbedding L3loc&rarrhk;L2 loc . In the third part of the thesis, we characterize bounded ancient solutions to the timedependent Stokes system with zero boundary value in various domains, including the half-space.

ISBN: 9781303275241Subjects--Topical Terms:

515831
Mathematics.

On some regularity problems in the theory of Navier Stokes equation.
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020 $a 9781303275241
035 $a (MiAaPQ)AAI3589053
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100 1 $a Jia, Hao. $3 1017558
245 1 0 $a On some regularity problems in the theory of Navier Stokes equation.
300 $a 73 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-11(E), Section: B.
500 $a Adviser: Vladimir Sverak.
502 $a Thesis (Ph.D.)--University of Minnesota, 2013.
520 $a We present some results obtained jointly with Professor Vladimir Sverak, in the study of some problems in the regularity theory of Navier Stokes equations, and some Liouville theorems for time-dependent Stokes system in domains jointly with Professor Vladimir Sverak and Gregory Seregin. In the first part of the thesis, we prove that the regularity of weak solution (called Leray solution) depends only locally on the regularity properties of the initial data, at least for a short time. This observation is then used to prove existence of scale-invariant solutions to the Navier Stokes equation with --1- homogeneous initial data without smallness condition. The main point of the result is that it seems to be out of reach of perturbation methods, and it provides valuable insights into the possible non-uniqueness of Leray-Hopf solutions, which is a long standing open problem in this area. In the second part of the thesis, we give a simple proof of the existence of initial data with minimal L3-norm for potential Navier-Stokes singularities, recently established in "Gallagher, I., Koch, G.S., Planchon, F., A profile decomposition approach to the Linfinityt&parl0;L3x &parr0; Navier-Stokes regularity criterion, Math. Ann. (published online July 2012)" with techniques based on profile decomposition. Our proof is more elementary, and is based on suitable splittings of initial data and energy methods. The main difficulty in the L3 case is the lack of compactness of the imbedding L3loc&rarrhk;L2 loc . In the third part of the thesis, we characterize bounded ancient solutions to the timedependent Stokes system with zero boundary value in various domains, including the half-space.
590 $a School code: 0130.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical Mathematics. $3 1672766
690 $a 0405
690 $a 0642
710 2 $a University of Minnesota. $b Mathematics. $3 1675975
773 0 $t Dissertation Abstracts International $g 74-11B(E).
790 $a 0130
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3589053