On the Free Surface Motion of Highly Subsonic Heat-Conducting Inviscid Flows

Luo, Tao; Zeng, Huihui

doi:10.1007/s00205-021-01624-9

Cited by 4 publications

(4 citation statements)

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“…Owing to the reflection symmetry of equations (17), we consider the Fourier series of solutions to the problem ( 17)-( 18) by expanding m(x 3 ) into…”

Section: It Is Seen That By Additionally Assuming λ2mentioning

confidence: 99%

“…Remark 2.4. It is seen from the proof above that Lemma 2.2 is essential for the construction of fundamental solutions to the homogeneous equations of (17). When λ+ = λ− , we can show the rows of A (k) (x 3 ), k = 1, 2, remain a basis of fundamental solutions if λ1 = λ± .…”

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confidence: 95%

“…From both physical and mathematical points of view, due to the second law of thermodynamics, the thermal conduction has an essential influence on the driving force to motions of fluids on free boundaries, cf. [17,18]. Hence, for the study of compressible fluid flow, it is fundamentally important to take the effects of entropy variation and heat transfer into consideration.…”

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confidence: 99%

“…[21,25]. Since only parts of the boundary values are prescribed by (18), we first identify the other unknowns by utilizing the fundamental solutions to the homogeneous equations of (17). In detail, because of the identity…”

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Resolvent problem for compressible Navier-Stokes equations with free surface

Huang,

Luo

2024

DCDS

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The motion of a compressible, viscous and heat-conducting fluid occupying an infinite layer, which is bounded below by a rigid bottom and above by a free surface, is described by a free boundary problem for the Navier-Stokes equations. We consider the associated resolvent equations with non-homogeneous boundary conditions arising from this free boundary problem. Different from the argument for the Cauchy problem where the solution can be obtained by utilizing the reflection symmetry of the Navier-Stokes equations directly, we derive an explicit representation of solutions to this boundary value problem, and the unknown boundary values are also well-characterized. Moreover, since the entropy variation and heat transfer effects make the problem much more intricate and challenging, the resolvent parameter needs to be treated more carefully than that for the isentropic Navier-Stokes equations. By analyzing each individual term in the solution formula, we establish the Lp estimates of solutions to the resolvent problem. Our result is the key and crucial step towards a further investigation of the free boundary problem for the full compressible Navier-Stokes equations by the semigroup approach.

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“…Owing to the reflection symmetry of equations (17), we consider the Fourier series of solutions to the problem ( 17)-( 18) by expanding m(x 3 ) into…”

Section: It Is Seen That By Additionally Assuming λ2mentioning

confidence: 99%

mentioning

confidence: 95%

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confidence: 99%

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confidence: 99%

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