A new sufficient condition for local regularity of a suitable weak solution to the MHD equations

Jiří Neustupa; Minsuk Yang

doi:10.1016/j.jmaa.2021.125258

A new sufficient condition for local regularity of a suitable weak solution to the MHD equations

Jiří Neustupa, Minsuk Yang

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We assume that Ω is either the whole space R³ or a half-space or a smooth bounded or exterior domain in R³, T>0 and (u,b,p) is a suitable weak solution of the MHD equations in Ω×(0,T). We show that (x₀,t₀)∈Ω×(0,T) is a regular point of the solution (u,b,p) if the limit inferior (for t→t₀−) of the sum of the L³–norms of u and b over an arbitrarily small ball B_ρ(x₀) is less than infinity.

Original language	English
Article number	125258
Journal	Journal of Mathematical Analysis and Applications
Volume	502
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2021.125258
Publication status	Published - 2021 Oct 15

Bibliographical note

Funding Information:
The first author has been supported by the Academy of Sciences of the Czech Republic ( RVO 67985840 ) and by the Grant Agency of the Czech Republic , grant No. GA19-04243S . The second author acknowledges the support of the National Research Foundation of Korea No. 2016R1C1B2015731 , No. 2015R1A5A1009350 , and the support of the Yonsei University No. 2019-22-0034 .

Publisher Copyright:
© 2021 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jmaa.2021.125258

Cite this

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title = "A new sufficient condition for local regularity of a suitable weak solution to the MHD equations",

abstract = "We assume that Ω is either the whole space R3 or a half-space or a smooth bounded or exterior domain in R3, T>0 and (u,b,p) is a suitable weak solution of the MHD equations in Ω×(0,T). We show that (x0,t0)∈Ω×(0,T) is a regular point of the solution (u,b,p) if the limit inferior (for t→t0−) of the sum of the L3–norms of u and b over an arbitrarily small ball Bρ(x0) is less than infinity.",

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AU - Yang, Minsuk

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N2 - We assume that Ω is either the whole space R3 or a half-space or a smooth bounded or exterior domain in R3, T>0 and (u,b,p) is a suitable weak solution of the MHD equations in Ω×(0,T). We show that (x0,t0)∈Ω×(0,T) is a regular point of the solution (u,b,p) if the limit inferior (for t→t0−) of the sum of the L3–norms of u and b over an arbitrarily small ball Bρ(x0) is less than infinity.

AB - We assume that Ω is either the whole space R3 or a half-space or a smooth bounded or exterior domain in R3, T>0 and (u,b,p) is a suitable weak solution of the MHD equations in Ω×(0,T). We show that (x0,t0)∈Ω×(0,T) is a regular point of the solution (u,b,p) if the limit inferior (for t→t0−) of the sum of the L3–norms of u and b over an arbitrarily small ball Bρ(x0) is less than infinity.

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A new sufficient condition for local regularity of a suitable weak solution to the MHD equations

Abstract

Bibliographical note

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