ASYMPTOTIC BEHAVIOR OF THE LINEARIZED PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE SURFACE

Yongting Huang

doi:10.3934/dcdsb.2024057

ASYMPTOTIC BEHAVIOR OF THE LINEARIZED PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE SURFACE

Yongting Huang^*

^*Corresponding author for this work

Harbin Institute of Technology

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

1 Scopus citations

Abstract

Deriving from the motion of a three-dimensional compressible viscous heat-conducting fluid in an infinite layer bounded above by a free surface, the paper is concerned with the asymptotic behavior of solutions to the linearized compressible Navier-Stokes equations in a strip domain. With the help of the explicit solution formula for the corresponding resolvent problem we have achieved, the time-decay estimates of solutions to this problem in L^p spaces, 2 ≤ p < ∞, are well established. Moreover, since we are interested in the linearized dynamic boundary condition of the surface wave problem, some exponential decay properties of the solutions are revealed. Our result is crucial and indispensable for developing the L^p theory for the free boundary problem of the full compressible Navier-Stokes equations.

Original language	English
Pages (from-to)	4569-4594
Number of pages	26
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	29
Issue number	11
DOIs	https://doi.org/10.3934/dcdsb.2024057
State	Published - Nov 2024
Externally published	Yes

Keywords

Navier-Stokes equations
decay estimates-L decay estimates.
free boundary condition
semigroup
thermal conduction

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10.3934/dcdsb.2024057

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title = "ASYMPTOTIC BEHAVIOR OF THE LINEARIZED PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE SURFACE",

abstract = "Deriving from the motion of a three-dimensional compressible viscous heat-conducting fluid in an infinite layer bounded above by a free surface, the paper is concerned with the asymptotic behavior of solutions to the linearized compressible Navier-Stokes equations in a strip domain. With the help of the explicit solution formula for the corresponding resolvent problem we have achieved, the time-decay estimates of solutions to this problem in Lp spaces, 2 ≤ p < ∞, are well established. Moreover, since we are interested in the linearized dynamic boundary condition of the surface wave problem, some exponential decay properties of the solutions are revealed. Our result is crucial and indispensable for developing the Lp theory for the free boundary problem of the full compressible Navier-Stokes equations.",

keywords = "Navier-Stokes equations, decay estimates-L decay estimates., free boundary condition, semigroup, thermal conduction",

author = "Yongting Huang",

year = "2024",

month = nov,

doi = "10.3934/dcdsb.2024057",

language = "英语",

volume = "29",

pages = "4569--4594",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

number = "11",

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T1 - ASYMPTOTIC BEHAVIOR OF THE LINEARIZED PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE SURFACE

AU - Huang, Yongting

PY - 2024/11

Y1 - 2024/11

N2 - Deriving from the motion of a three-dimensional compressible viscous heat-conducting fluid in an infinite layer bounded above by a free surface, the paper is concerned with the asymptotic behavior of solutions to the linearized compressible Navier-Stokes equations in a strip domain. With the help of the explicit solution formula for the corresponding resolvent problem we have achieved, the time-decay estimates of solutions to this problem in Lp spaces, 2 ≤ p < ∞, are well established. Moreover, since we are interested in the linearized dynamic boundary condition of the surface wave problem, some exponential decay properties of the solutions are revealed. Our result is crucial and indispensable for developing the Lp theory for the free boundary problem of the full compressible Navier-Stokes equations.

AB - Deriving from the motion of a three-dimensional compressible viscous heat-conducting fluid in an infinite layer bounded above by a free surface, the paper is concerned with the asymptotic behavior of solutions to the linearized compressible Navier-Stokes equations in a strip domain. With the help of the explicit solution formula for the corresponding resolvent problem we have achieved, the time-decay estimates of solutions to this problem in Lp spaces, 2 ≤ p < ∞, are well established. Moreover, since we are interested in the linearized dynamic boundary condition of the surface wave problem, some exponential decay properties of the solutions are revealed. Our result is crucial and indispensable for developing the Lp theory for the free boundary problem of the full compressible Navier-Stokes equations.

KW - Navier-Stokes equations

KW - decay estimates-L decay estimates.

KW - free boundary condition

KW - semigroup

KW - thermal conduction

UR - https://www.scopus.com/pages/publications/85197492709

U2 - 10.3934/dcdsb.2024057

DO - 10.3934/dcdsb.2024057

M3 - 文章

AN - SCOPUS:85197492709

SN - 1531-3492

VL - 29

SP - 4569

EP - 4594

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 11

ER -

ASYMPTOTIC BEHAVIOR OF THE LINEARIZED PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE SURFACE

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Keywords

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