On Caccioppoli's inequalities of Stokes equations and Navier-Stokes equations near boundary

Tongkeun Chang; Kyungkeun Kang

doi:10.1016/j.jde.2020.05.013

On Caccioppoli's inequalities of Stokes equations and Navier-Stokes equations near boundary

Tongkeun Chang, Kyungkeun Kang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study Caccioppoli's inequalities of the non-stationary Stokes equations and Navier-Stokes equations. Our analysis is local near boundary and we prove that, in contrast to the interior case, the Caccioppoli's inequalities of the Stokes equations and the Navier-Stokes equations, in general, fail near boundary.

Original language	English
Pages (from-to)	6732-6757
Number of pages	26
Journal	Journal of Differential Equations
Volume	269
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2020.05.013
Publication status	Published - 2020 Oct 15

Bibliographical note

Funding Information:
T. Chang is partially supported by NRF-2017R1D1A1B03033427 and K. Kang is partially supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350.

Funding Information:
T. Chang is partially supported by NRF - 2017R1D1A1B03033427 and K. Kang is partially supported by NRF - 2019R1A2C1084685 and NRF - 2015R1A5A1009350 .

Publisher Copyright:
© 2020 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2020.05.013

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title = "On Caccioppoli's inequalities of Stokes equations and Navier-Stokes equations near boundary",

abstract = "We study Caccioppoli's inequalities of the non-stationary Stokes equations and Navier-Stokes equations. Our analysis is local near boundary and we prove that, in contrast to the interior case, the Caccioppoli's inequalities of the Stokes equations and the Navier-Stokes equations, in general, fail near boundary.",

author = "Tongkeun Chang and Kyungkeun Kang",

note = "Funding Information: T. Chang is partially supported by NRF-2017R1D1A1B03033427 and K. Kang is partially supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350. Funding Information: T. Chang is partially supported by NRF - 2017R1D1A1B03033427 and K. Kang is partially supported by NRF - 2019R1A2C1084685 and NRF - 2015R1A5A1009350 . Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = oct,

day = "15",

doi = "10.1016/j.jde.2020.05.013",

language = "English",

volume = "269",

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journal = "Journal of Differential Equations",

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T1 - On Caccioppoli's inequalities of Stokes equations and Navier-Stokes equations near boundary

AU - Chang, Tongkeun

AU - Kang, Kyungkeun

N1 - Funding Information: T. Chang is partially supported by NRF-2017R1D1A1B03033427 and K. Kang is partially supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350. Funding Information: T. Chang is partially supported by NRF - 2017R1D1A1B03033427 and K. Kang is partially supported by NRF - 2019R1A2C1084685 and NRF - 2015R1A5A1009350 . Publisher Copyright: © 2020 Elsevier Inc.

PY - 2020/10/15

Y1 - 2020/10/15

N2 - We study Caccioppoli's inequalities of the non-stationary Stokes equations and Navier-Stokes equations. Our analysis is local near boundary and we prove that, in contrast to the interior case, the Caccioppoli's inequalities of the Stokes equations and the Navier-Stokes equations, in general, fail near boundary.

AB - We study Caccioppoli's inequalities of the non-stationary Stokes equations and Navier-Stokes equations. Our analysis is local near boundary and we prove that, in contrast to the interior case, the Caccioppoli's inequalities of the Stokes equations and the Navier-Stokes equations, in general, fail near boundary.

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DO - 10.1016/j.jde.2020.05.013

M3 - Article

AN - SCOPUS:85085740759

SN - 0022-0396

VL - 269

SP - 6732

EP - 6757

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 9

ER -

On Caccioppoli's inequalities of Stokes equations and Navier-Stokes equations near boundary

Abstract

Bibliographical note

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