Existence of suitable weak solutions to the Navier–Stokes equations in time varying domains

Hi Jun Choe; Yunsoo Jang; Minsuk Yang

doi:10.1016/j.na.2017.08.003

Existence of suitable weak solutions to the Navier–Stokes equations in time varying domains

Hi Jun Choe, Yunsoo Jang, Minsuk Yang

Department of Mathematics

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

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Abstract

We consider suitable weak solutions to the Navier–Stokes equations in time varying domains. We develop Schauder theory for the approximate Stokes equations in time varying domains whose solutions satisfy a uniform localized energy estimate including boundary. Existence of suitable weak solutions in time varying domains follows from compactness in Lebesgue and Sobolev spaces.

Original language	English
Pages (from-to)	163-176
Number of pages	14
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	163
DOIs	https://doi.org/10.1016/j.na.2017.08.003
Publication status	Published - 2017 Nov

Bibliographical note

Funding Information:
The authors would like to express their sincere gratitude to the referee for careful reading and for many helpful comments. Hi Jun Choe has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1A5A1009350 ). Yunsoo Jang has been supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2016R1D1A1B03935364 ). Minsuk Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B2015731 ).

Publisher Copyright:
© 2017 Elsevier Ltd

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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title = "Existence of suitable weak solutions to the Navier–Stokes equations in time varying domains",

abstract = "We consider suitable weak solutions to the Navier–Stokes equations in time varying domains. We develop Schauder theory for the approximate Stokes equations in time varying domains whose solutions satisfy a uniform localized energy estimate including boundary. Existence of suitable weak solutions in time varying domains follows from compactness in Lebesgue and Sobolev spaces.",

author = "Choe, {Hi Jun} and Yunsoo Jang and Minsuk Yang",

note = "Funding Information: The authors would like to express their sincere gratitude to the referee for careful reading and for many helpful comments. Hi Jun Choe has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1A5A1009350 ). Yunsoo Jang has been supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2016R1D1A1B03935364 ). Minsuk Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B2015731 ). Publisher Copyright: {\textcopyright} 2017 Elsevier Ltd",

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doi = "10.1016/j.na.2017.08.003",

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AU - Jang, Yunsoo

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AB - We consider suitable weak solutions to the Navier–Stokes equations in time varying domains. We develop Schauder theory for the approximate Stokes equations in time varying domains whose solutions satisfy a uniform localized energy estimate including boundary. Existence of suitable weak solutions in time varying domains follows from compactness in Lebesgue and Sobolev spaces.

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Existence of suitable weak solutions to the Navier–Stokes equations in time varying domains

Abstract

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