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May/June 2021 The global well-posedness of the compressible fluid model of Korteweg type for the critical case
Takayuki Kobayashi, Miho Murata
Differential Integral Equations 34(5/6): 245-264 (May/June 2021).

Abstract

In this paper, we consider the compressible fluid model of Korteweg type in a critical case where the derivative of pressure equals $0$ at a given constant state. We show that the system admits a unique, global strong solution for small initial data in the maximal $L_p$-$L_q$ regularity class. Consequently, we also prove the decay estimates of the solutions to the nonlinear problem. To obtain the global well-posedness for the critical case, we show $L_p$-$L_q$ decay properties of solutions to the linearized equations under an additional assumption for low frequencies.

Citation

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Takayuki Kobayashi. Miho Murata. "The global well-posedness of the compressible fluid model of Korteweg type for the critical case." Differential Integral Equations 34 (5/6) 245 - 264, May/June 2021.

Information

Published: May/June 2021
First available in Project Euclid: 15 April 2021

Subjects:
Primary: 35Q30, 76N10

Rights: Copyright © 2021 Khayyam Publishing, Inc.

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Vol.34 • No. 5/6 • May/June 2021
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