Blowup Criterion for Viscous Baratropic Flows with Vacuum States

Abstract We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stoke...
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Autor*in:	Huang, Xiangdi [verfasserIn] Li, Jing Xin, Zhouping

Format:	Artikel
Sprache:	Englisch

Erschienen:	2010

Schlagwörter:	Weak Solution Global Existence Strong Solution Smooth Solution Local Existence

Anmerkung:	© Springer-Verlag 2010

Übergeordnetes Werk:	Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 301(2010), 1 vom: 09. Okt., Seite 23-35
Übergeordnetes Werk:	volume:301 ; year:2010 ; number:1 ; day:09 ; month:10 ; pages:23-35

Links:	Volltext

DOI / URN:	10.1007/s00220-010-1148-y

Katalog-ID:	OLC2038899347

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520			\|a Abstract We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases.
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allfields	10.1007/s00220-010-1148-y doi (DE-627)OLC2038899347 (DE-He213)s00220-010-1148-y-p DE-627 ger DE-627 rakwb eng 530 510 VZ Huang, Xiangdi verfasserin aut Blowup Criterion for Viscous Baratropic Flows with Vacuum States 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2010 Abstract We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases. Weak Solution Global Existence Strong Solution Smooth Solution Local Existence Li, Jing aut Xin, Zhouping aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 301(2010), 1 vom: 09. Okt., Seite 23-35 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:301 year:2010 number:1 day:09 month:10 pages:23-35 https://doi.org/10.1007/s00220-010-1148-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 301 2010 1 09 10 23-35
spelling	10.1007/s00220-010-1148-y doi (DE-627)OLC2038899347 (DE-He213)s00220-010-1148-y-p DE-627 ger DE-627 rakwb eng 530 510 VZ Huang, Xiangdi verfasserin aut Blowup Criterion for Viscous Baratropic Flows with Vacuum States 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2010 Abstract We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases. Weak Solution Global Existence Strong Solution Smooth Solution Local Existence Li, Jing aut Xin, Zhouping aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 301(2010), 1 vom: 09. Okt., Seite 23-35 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:301 year:2010 number:1 day:09 month:10 pages:23-35 https://doi.org/10.1007/s00220-010-1148-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 301 2010 1 09 10 23-35
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allfieldsSound	10.1007/s00220-010-1148-y doi (DE-627)OLC2038899347 (DE-He213)s00220-010-1148-y-p DE-627 ger DE-627 rakwb eng 530 510 VZ Huang, Xiangdi verfasserin aut Blowup Criterion for Viscous Baratropic Flows with Vacuum States 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2010 Abstract We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases. Weak Solution Global Existence Strong Solution Smooth Solution Local Existence Li, Jing aut Xin, Zhouping aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 301(2010), 1 vom: 09. Okt., Seite 23-35 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:301 year:2010 number:1 day:09 month:10 pages:23-35 https://doi.org/10.1007/s00220-010-1148-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 301 2010 1 09 10 23-35
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title_sort	blowup criterion for viscous baratropic flows with vacuum states
title_auth	Blowup Criterion for Viscous Baratropic Flows with Vacuum States
abstract	Abstract We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases. © Springer-Verlag 2010
abstractGer	Abstract We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases. © Springer-Verlag 2010
abstract_unstemmed	Abstract We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases. © Springer-Verlag 2010
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title_short	Blowup Criterion for Viscous Baratropic Flows with Vacuum States
url	https://doi.org/10.1007/s00220-010-1148-y
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author2	Li, Jing Xin, Zhouping
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doi_str	10.1007/s00220-010-1148-y
up_date	2024-07-03T20:46:53.282Z
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