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Some Quantitative Regularity Theorems for the Navier-Stokes Equations.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Some Quantitative Regularity Theorems for the Navier-Stokes Equations.
作者:	Palasek, Stanley.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, 2023
面頁冊數:	178 p.
附註:	Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
附註:	Advisor: Tao, Terence Chi-Shen.
Contained By:	Dissertations Abstracts International84-12B.
標題:	Mathematics.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30528063
ISBN:	9798379709662

Some Quantitative Regularity Theorems for the Navier-Stokes Equations.
Palasek, Stanley.

Some Quantitative Regularity Theorems for the Navier-Stokes Equations. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 178 p.

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2023.

This item must not be sold to any third party vendors.

Consider a velocity field u solving the incompressible Navier-Stokes equations on [0, T] x ℝd (d ≥ 3) and satisfying ∥u(t)∥X ≤ A for all times, where the norm X is critical with respect to the Navier-Stokes scaling. We prove several theorems to the effect that the regularity of the solution can be controlled explicitly in terms of A, building upon Tao’s pioneering work on the case d = 3, X = L 3 (ℝ3 ). First we prove a generalization to the critical Lebesgue space in any number of spatial dimensions (d ≥ 4, X = Ld (ℝd )). Then we show a variety of circumstances under which Tao’s bounds can be strengthened, including the case in which the solution is nearly axisymmetric. For exactly axisymmetric solutions, we prove regularity in terms of the weak norm X = L 3,∞(ℝ3 ) which implies effective bounds on approximately self-similar behavior.

ISBN: 9798379709662Subjects--Topical Terms:

184409
Mathematics.
Subjects--Index Terms:

Fluids

Some Quantitative Regularity Theorems for the Navier-Stokes Equations.
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300 $a 178 p.
500 $a Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
500 $a Advisor: Tao, Terence Chi-Shen.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a Consider a velocity field u solving the incompressible Navier-Stokes equations on [0, T] x ℝd (d ≥ 3) and satisfying ∥u(t)∥X ≤ A for all times, where the norm X is critical with respect to the Navier-Stokes scaling. We prove several theorems to the effect that the regularity of the solution can be controlled explicitly in terms of A, building upon Tao’s pioneering work on the case d = 3, X = L 3 (ℝ3 ). First we prove a generalization to the critical Lebesgue space in any number of spatial dimensions (d ≥ 4, X = Ld (ℝd )). Then we show a variety of circumstances under which Tao’s bounds can be strengthened, including the case in which the solution is nearly axisymmetric. For exactly axisymmetric solutions, we prove regularity in terms of the weak norm X = L 3,∞(ℝ3 ) which implies effective bounds on approximately self-similar behavior.
590 $a School code: 0031.
650 4 $a Mathematics. $3 184409
650 4 $a Applied mathematics. $3 377601
653 $a Fluids
653 $a Navier-Stokes equations
653 $a PDE
653 $a Regularity
653 $a Navier-Stokes scaling
690 $a 0405
690 $a 0364
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 708654
773 0 $t Dissertations Abstracts International $g 84-12B.
790 $a 0031
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30528063