Classical solutions for fractional porous medium flow

Young Pil Choi; In Jee Jeong

doi:10.1016/j.na.2021.112393

Classical solutions for fractional porous medium flow

Young Pil Choi, In Jee Jeong

Department of Mathematics

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

5 Citations (Scopus)

Abstract

We consider the fractional porous medium flow introduced by Caffarelli and Vazquez (2011) and obtain local in time existence, uniqueness, and blow-up criterion for smooth solutions. The proof is based on establishing a commutator estimate involving fractional Laplacian operators.

Original language	English
Article number	112393
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	210
DOIs	https://doi.org/10.1016/j.na.2021.112393
Publication status	Published - 2021 Sept

Bibliographical note

Funding Information:
We thank Sung-Jin Oh for helpful conversations regarding degenerate parabolic equations and pseudo-differential calculus. YPC has been supported by NRF, Republic of Korea grant (No. 2017R1C1B2012918 ), POSCO Science Fellowship of POSCO TJ Park Foundation , and Yonsei University Research Fund of 2019-22-0212 and 2020-22-0505. IJJ has been supported by the New Faculty Startup Fund from Seoul National University, Republic of Korea , the Science Fellowship of POSCO TJ Park Foundation, and the National Research Foundation of Korea grant (No. 2019R1F1A1058486 ).

Publisher Copyright:
© 2021 Elsevier Ltd

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.na.2021.112393

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title = "Classical solutions for fractional porous medium flow",

abstract = "We consider the fractional porous medium flow introduced by Caffarelli and Vazquez (2011) and obtain local in time existence, uniqueness, and blow-up criterion for smooth solutions. The proof is based on establishing a commutator estimate involving fractional Laplacian operators.",

author = "Choi, {Young Pil} and Jeong, {In Jee}",

note = "Funding Information: We thank Sung-Jin Oh for helpful conversations regarding degenerate parabolic equations and pseudo-differential calculus. YPC has been supported by NRF, Republic of Korea grant (No. 2017R1C1B2012918 ), POSCO Science Fellowship of POSCO TJ Park Foundation , and Yonsei University Research Fund of 2019-22-0212 and 2020-22-0505. IJJ has been supported by the New Faculty Startup Fund from Seoul National University, Republic of Korea , the Science Fellowship of POSCO TJ Park Foundation, and the National Research Foundation of Korea grant (No. 2019R1F1A1058486 ). Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2021",

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doi = "10.1016/j.na.2021.112393",

language = "English",

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journal = "Nonlinear Analysis, Theory, Methods and Applications",

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T1 - Classical solutions for fractional porous medium flow

AU - Choi, Young Pil

AU - Jeong, In Jee

N1 - Funding Information: We thank Sung-Jin Oh for helpful conversations regarding degenerate parabolic equations and pseudo-differential calculus. YPC has been supported by NRF, Republic of Korea grant (No. 2017R1C1B2012918 ), POSCO Science Fellowship of POSCO TJ Park Foundation , and Yonsei University Research Fund of 2019-22-0212 and 2020-22-0505. IJJ has been supported by the New Faculty Startup Fund from Seoul National University, Republic of Korea , the Science Fellowship of POSCO TJ Park Foundation, and the National Research Foundation of Korea grant (No. 2019R1F1A1058486 ). Publisher Copyright: © 2021 Elsevier Ltd

PY - 2021/9

Y1 - 2021/9

N2 - We consider the fractional porous medium flow introduced by Caffarelli and Vazquez (2011) and obtain local in time existence, uniqueness, and blow-up criterion for smooth solutions. The proof is based on establishing a commutator estimate involving fractional Laplacian operators.

AB - We consider the fractional porous medium flow introduced by Caffarelli and Vazquez (2011) and obtain local in time existence, uniqueness, and blow-up criterion for smooth solutions. The proof is based on establishing a commutator estimate involving fractional Laplacian operators.

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DO - 10.1016/j.na.2021.112393

M3 - Article

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VL - 210

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 112393

ER -

Classical solutions for fractional porous medium flow

Abstract

Bibliographical note

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