On the Maximal Lp-Lq Regularity Theorem for the Linearized Electro-Magnetic Field Equations with Interface Conditions

E. Frolova*, Y. Shibata

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This paper deals with the maximal Lp-Lq regularity theorem for the linearized electro-magnetic field equations with interface conditions and perfect wall condition. This problem is motivated by linearization of the coupled magnetohydrodynamics system which generates two separate problems. The first problem is associated with well studied Stokes system. Another problem related to the magnetic field is studied in this paper. The maximal Lp-Lq regularity theorem for the Stokes equations with interface and nonslip boundary conditions has been proved by Pruess and Simonett (2016), and Maryani and Saito (2017). Combination of these results and the result obtained in the present paper yields local well-posedness for the MHD problem in the case of two incompressible liquids separated by a closed interface. It is planned to prove it in a forthcoming paper. The main part of the present paper is devoted to proving the existence of R-bounded solution operators associated with generalized resolvent problem. The maximal Lp-Lq regularity is established by applying the Weis operator-valued Fourier multiplier theorem.

Original languageEnglish
Pages (from-to)87-117
Number of pages31
JournalJournal of Mathematical Sciences
Volume260
Issue number1
DOIs
Publication statusPublished - 2022 Jan

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On the Maximal Lp-Lq Regularity Theorem for the Linearized Electro-Magnetic Field Equations with Interface Conditions'. Together they form a unique fingerprint.

Cite this