Local strong solution of Navier–Stokes–Poisson equations with degenerated viscosity coefficient

Di, Qianqian

doi:10.1002/mma.3354

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…Only recently, the local well-posedness theory for inviscid flows is developed by Coutand, Lindblad and Shkoller [7,8,9], Jang and Masmoudi [24,25], Gu and Lei [13,14], Luo, Xin and Zeng [39] in variant settings. See [22,10] for the viscous case. The nonlinear stabilities of some special solutions in variant settings with the physical vacuum condition can be found in [17,18,36,37,40,41,42,46,59,60].…”

Section: Introductionmentioning

confidence: 99%

Local Existence and Uniqueness of Strong Solutions to the Free Boundary Problem of the Full Compressible Navier--Stokes Equations in three dimensions

Liu¹,

Yuan²

2019

SIAM J. Math. Anal.

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In this paper we establish the local-in-time existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in three-dimensional space. The vanishing density and temperature condition is imposed on the free boundary, which captures the motions of the non-isentropic viscous gas surrounded by vacuum with bounded entropy. We also assume some proper decay rates of the density towards the boundary and singularities of derivatives of the temperature across the boundary on the initial data, which coincides with the physical vacuum condition for the isentropic flows. This extends the previous result of Liu [arXiv:1612.07936] by removing the spherically symmetric assumption and considering more general initial density and temperature profiles.|∂ 2 t a| J −1 |Dv t ||a| 2 + J −2 |Dv| 2 |a| 3 , |∂a| J

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Section: Introductionmentioning

confidence: 99%

Local Existence and Uniqueness of Strong Solutions to the Free Boundary Problem of the Full Compressible Navier--Stokes Equations in three dimensions

Liu¹,

Yuan²

2019

SIAM J. Math. Anal.

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On the physical vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation

Li,

Wang

2024

Journal of Mathematical Physics

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This paper is concerned with the vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation. We establish the local-in-time well-posedness of classical solutions to this system, and the solutions possess higher-order regularity all the way to the vacuum free boundary, though the density degenerates near the vacuum boundary. To deal with the force term generated by the Poisson equation, we make use of the structure of the momentum equation formulated in a fixed domain by the Lagrangian coordinates. The proof is built on some higher-order weighted energy functionals and weighted embeddings corresponding to the degeneracy near the initial vacuum boundary.

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Local strong solution of Navier–Stokes–Poisson equations with degenerated viscosity coefficient

Cited by 2 publications

References 27 publications

Local Existence and Uniqueness of Strong Solutions to the Free Boundary Problem of the Full Compressible Navier--Stokes Equations in three dimensions

Local Existence and Uniqueness of Strong Solutions to the Free Boundary Problem of the Full Compressible Navier--Stokes Equations in three dimensions

On the physical vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation

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