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Approximation via Degree Reduction o...

Enlow, Matthew,

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Approximation via Degree Reduction of Nonlinearities With Applications to Turbulent Flows, Flame Fronts, and Magnetohydrodynamics /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Approximation via Degree Reduction of Nonlinearities With Applications to Turbulent Flows, Flame Fronts, and Magnetohydrodynamics // Matthew Enlow.
Author:	Enlow, Matthew,
Description:	1 electronic resource (166 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-11, Section: B.
Contained By:	Dissertations Abstracts International85-11B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31293749
ISBN:	9798382583877

Approximation via Degree Reduction of Nonlinearities With Applications to Turbulent Flows, Flame Fronts, and Magnetohydrodynamics /
Enlow, Matthew,

Approximation via Degree Reduction of Nonlinearities With Applications to Turbulent Flows, Flame Fronts, and Magnetohydrodynamics /Matthew Enlow. - 1 electronic resource (166 pages)

Source: Dissertations Abstracts International, Volume: 85-11, Section: B.

We perform an analytical and computational investigation on the effectiveness of a locally bounded truncation function, which we call a calming function, when applied to the nonlinear terms of several dissipative partial differential equations. In particular, the 3D Navier-Stokes equations of incompressible fluid flow, the 2D Kuramoto-Sivashinsky equations of laminar flame fronts, and the 2D MHD-Boussinesq equations of magnetohydrodynamics. Each of these equations have open questions about the global existence and uniqueness of their solutions. These calming functions effectively reduce the algebraic degree of select nonlinear terms, thus one can verify global wellposedness for these "calmed systems". More specifically, in this work we show analytically in this work that the solutions to the calmed systems are globally well-posed, have higher-order regularity, and converge to solutions of the original models on short-time intervals as an introduced parameter in the calmed system tends to 0. We obtain additional results in the case of the 3D Calmed Navier-Stokes equations: when applying calming to the nonlinear term written in its rotational form, we and that the dynamical system generated by the calmed NSE in the rotational form possesses both an energy identity and a global attractor. Moreover, for calmed Navier-Stokes written either in its advective form or rotational form, we show that strong solutions to the calmed equations converge to strong solutions of the NSE without assuming their existence, providing a new proof of the short-time existence of strong solutions to the 3D Navier-Stokes equations.

English

ISBN: 9798382583877Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Calming function

Approximation via Degree Reduction of Nonlinearities With Applications to Turbulent Flows, Flame Fronts, and Magnetohydrodynamics /
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245 1 0 $a Approximation via Degree Reduction of Nonlinearities With Applications to Turbulent Flows, Flame Fronts, and Magnetohydrodynamics / $c Matthew Enlow.
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500 $a Advisors: Larios, Adam Committee members: Avalos, George; Foss, Mikil; Pitts, David; Park, Jae Sung.
502 $b Ph.D. $c The University of Nebraska - Lincoln $d 2024.
520 $a We perform an analytical and computational investigation on the effectiveness of a locally bounded truncation function, which we call a calming function, when applied to the nonlinear terms of several dissipative partial differential equations. In particular, the 3D Navier-Stokes equations of incompressible fluid flow, the 2D Kuramoto-Sivashinsky equations of laminar flame fronts, and the 2D MHD-Boussinesq equations of magnetohydrodynamics. Each of these equations have open questions about the global existence and uniqueness of their solutions. These calming functions effectively reduce the algebraic degree of select nonlinear terms, thus one can verify global wellposedness for these "calmed systems". More specifically, in this work we show analytically in this work that the solutions to the calmed systems are globally well-posed, have higher-order regularity, and converge to solutions of the original models on short-time intervals as an introduced parameter in the calmed system tends to 0. We obtain additional results in the case of the 3D Calmed Navier-Stokes equations: when applying calming to the nonlinear term written in its rotational form, we and that the dynamical system generated by the calmed NSE in the rotational form possesses both an energy identity and a global attractor. Moreover, for calmed Navier-Stokes written either in its advective form or rotational form, we show that strong solutions to the calmed equations converge to strong solutions of the NSE without assuming their existence, providing a new proof of the short-time existence of strong solutions to the 3D Navier-Stokes equations.
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650 4 $a Mathematics. $3 515831
650 4 $a Physics. $3 516296
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mechanics. $3 525881
653 $a Calming function
653 $a Fluid flow
653 $a Navier-Stokes equations
653 $a Turbulence
690 $a 0405
690 $a 0346
690 $a 0605
690 $a 0364
710 2 $a The University of Nebraska - Lincoln. $b Mathematics. $e degree granting institution. $3 3816299
720 1 $a Larios, Adam $e degree supervisor.
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790 $a 0138
791 $a Ph.D.
792 $a 2024
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