Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas

Tsukasa Iwabuchi; Takayoshi Ogawa

doi:10.1007/s41808-021-00136-7

Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas

Tsukasa Iwabuchi, Takayoshi Ogawa

SCI - Mathematics

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

2 Citations (Scopus)

Abstract

We study the ill-posedness issue for the compressible viscous heat-conductive flows in two dimensions. In the scaling invariant spaces, negative regularity of the temperature causes an essential problem for the well-posedness, and the ill-posedness is obtained for all integrability indices except for the L¹ case.

Original language	English
Pages (from-to)	571-587
Number of pages	17
Journal	Journal of Elliptic and Parabolic Equations
Volume	7
Issue number	2
DOIs	https://doi.org/10.1007/s41808-021-00136-7
Publication status	Published - 2021 Dec

Keywords

Compressible Navier-Stokes equations
Critical Besov spaces
Discontinuity
Ideal gas
Ill-posedness
The Cauchy problem

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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10.1007/s41808-021-00136-7

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title = "Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas",

abstract = "We study the ill-posedness issue for the compressible viscous heat-conductive flows in two dimensions. In the scaling invariant spaces, negative regularity of the temperature causes an essential problem for the well-posedness, and the ill-posedness is obtained for all integrability indices except for the L1 case.",

keywords = "Compressible Navier-Stokes equations, Critical Besov spaces, Discontinuity, Ideal gas, Ill-posedness, The Cauchy problem",

author = "Tsukasa Iwabuchi and Takayoshi Ogawa",

note = "Funding Information: The first author was supported by JSPS Grant-in-Aid for Young Scientists (A) (No. 17H04824). The second author was supported by JSPS Grant-in-Aid, Scientific Research (S) (No. 19H05597) and JSPS Challenging Research (Pioneering) (No. 20K20284). Publisher Copyright: {\textcopyright} 2021, Orthogonal Publisher and Springer Nature Switzerland AG.",

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doi = "10.1007/s41808-021-00136-7",

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T1 - Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas

AU - Iwabuchi, Tsukasa

AU - Ogawa, Takayoshi

N1 - Funding Information: The first author was supported by JSPS Grant-in-Aid for Young Scientists (A) (No. 17H04824). The second author was supported by JSPS Grant-in-Aid, Scientific Research (S) (No. 19H05597) and JSPS Challenging Research (Pioneering) (No. 20K20284). Publisher Copyright: © 2021, Orthogonal Publisher and Springer Nature Switzerland AG.

PY - 2021/12

Y1 - 2021/12

N2 - We study the ill-posedness issue for the compressible viscous heat-conductive flows in two dimensions. In the scaling invariant spaces, negative regularity of the temperature causes an essential problem for the well-posedness, and the ill-posedness is obtained for all integrability indices except for the L1 case.

AB - We study the ill-posedness issue for the compressible viscous heat-conductive flows in two dimensions. In the scaling invariant spaces, negative regularity of the temperature causes an essential problem for the well-posedness, and the ill-posedness is obtained for all integrability indices except for the L1 case.

KW - Compressible Navier-Stokes equations

KW - Critical Besov spaces

KW - Discontinuity

KW - Ideal gas

KW - Ill-posedness

KW - The Cauchy problem

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JO - Journal of Elliptic and Parabolic Equations

JF - Journal of Elliptic and Parabolic Equations

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ER -

Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas

Abstract

Keywords

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