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Some Quantitative Regularity Theorems for the Navier-Stokes Equations.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Some Quantitative Regularity Theorems for the Navier-Stokes Equations./
Author:	Palasek, Stanley.
Description:	1 online resource (178 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
Contained By:	Dissertations Abstracts International84-12B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798379709662

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

Some Quantitative Regularity Theorems for the Navier-Stokes Equations. - 1 online resource (178 pages)

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

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

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798379709662Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

FluidsIndex Terms--Genre/Form:

554714
Electronic books.

Some Quantitative Regularity Theorems for the Navier-Stokes Equations.
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245 1 0 $a Some Quantitative Regularity Theorems for the Navier-Stokes Equations.
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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.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Applied mathematics. $3 1069907
653 $a Fluids
653 $a Navier-Stokes equations
653 $a PDE
653 $a Regularity
653 $a Navier-Stokes scaling
655 7 $a Electronic books. $2 local $3 554714
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690 $a 0364
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773 0 $t Dissertations Abstracts International $g 84-12B.
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