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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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$L_p$-estimates of solution of the free boundary problem for viscous compressible and incompressible fluids in the linear approximation
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by V. A. Solonnikov
St. Petersburg Math. J. 32, 577-604
DOI: https://doi.org/10.1090/spmj/1663
Published electronically: May 11, 2021
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Abstract:

The paper contains $L_p$-estimates and a theorem on the local in time solvability of the problem arising as a result of linearization of the free boundary problem for two viscous fluids, compressible and incompressible, contained in a bounded vessel, separated by a free interface, and subject to mass and capillary forces. This result is known for the case of $p=2$; it serves as an analytical basis for the study of the complete nonlinear problem. The proof is based on the “maximal regularity” estimate of the solution obtained with the help of the $L_p$ Fourier multiplier theorem due to P. I. Lizorkin.
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Bibliographic Information
  • V. A. Solonnikov
  • Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
  • MR Author ID: 194906
  • Email: solonnik@pdmi.ras.ru
  • Received by editor(s): October 3, 2019
  • Published electronically: May 11, 2021
  • Additional Notes: Supported by RFBR grant no. 20-01-00397

    • Dedicated: Dedicated to Nina Nikolaevna Ural’tseva on the occasion of her $85$th birthday.
  • © Copyright 2021 American Mathematical Society
  • Journal: St. Petersburg Math. J. 32, 577-604
  • MSC (2020): Primary 35R35; Secondary 76D27
  • DOI: https://doi.org/10.1090/spmj/1663
  • MathSciNet review: 4099102