Boundary layer problems for the two-dimensional compressible Navier–Stokes equations

Gong, Shengbo; Guo, Yan; Wang, Yaguang

doi:10.1142/s0219530515400011

Cited by 19 publications

(8 citation statements)

References 9 publications

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“…[18,3,19]. Limited to isentropic viscous fluids, where there is no thermal layer, the boundary layer can be described by a Prandtl-type system, and its wellposedness theory with respect to two space variables is established by Wang-Xie-Yang [34] and Gong-Guo-Wang [12] independently under the same monotonicity condition as the Prandtl equations. Very recently, Liu-Wang-Yang [24] studied the behavior of both viscous layer and thermal layer for two-dimensional non-isentropic compressible fluids in different viscosity and heat conductivity limits.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Local-in-time well-posedness for compressible MHD boundary layer

Huang

Liu

Yang

2019

Journal of Differential Equations

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In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane, with no-slip condition for velocity field, perfect conducting condition for magnetic field and Dirichlet boundary condition for temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer that is described by a Prandtl-type system. By applying a coordinate transformation in terms of stream function as motivated by the recent work [26] on the incompressible MHD system, under the non-degeneracy condition on the tangential magnetic field, we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.2010 Mathematics Subject Classification. 35A07, 35M33, 35Q35, 76N20, 76W05.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Local-in-time well-posedness for compressible MHD boundary layer

Huang

Liu

Yang

2019

Journal of Differential Equations

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“…Mathematical analysis on the boundary layer theory has been extensively studied in different contexts, cf. [1,4,3,5,6,7,8,9,10,11,16,17,21,22,23,27,28,29,30,31,34,35,36,37,40,42] and the references therein for incompressible or compressible Navier-Stokes boundary layer. Boundary layer problem on some more complex fluids such as magnetohydrodynamic was also made great progresses, cf.…”

Section: Introductionmentioning

confidence: 99%

Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow

Fan

Liu

Ruan

2021

era

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<p style='text-indent:20px;'>In this paper, we consider the two-dimensional (2D) two-fluid boundary layer system, which is a hyperbolic-degenerate parabolic-elliptic coupling system derived from the compressible isentropic two-fluid flow equations with nonslip boundary condition for the velocity. The local existence and uniqueness is established in weighted Sobolev spaces under the monotonicity assumption on tangential velocity along normal direction based on a nonlinear energy method by employing a nonlinear cancelation technic introduced in [R. Alexandre, Y.-G. Wang, C.-J. Xu and T. Yang, J. Amer. Math. Soc., 28 (2015), 745-784; N. Masmoudi and T.K. Wong, Comm. Pure Appl. Math., 68(2015), 1683-1741] and developed in [C.-J. Liu, F. Xie and T. Yang, Comm. Pure Appl. Math., 72(2019), 63-121].</p>

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“…And we also refer to [10,32,35] for the inviscid limit of incompressible MHD system with Navier-slip boundary conditions. However, when the velocity is given the no-slip boundary condition, in general the strong boundary layer must occur [11,17,24,25,26,34]. Consequently, the inviscid limit in L ∞ sense becomes dramatically difficult due to the uncontrollability of the vorticity of strong boundary layer as the coefficient of viscosity goes to zero.…”

Section: Introductionmentioning

confidence: 99%

Uniform regularity estimates and invisicid limit for the compressible non-resistive magnetohydrodynamics system

Cui¹,

Sheng-xin²,

Xie³

2021

Preprint

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We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the assumption that the initial magnetic field is transverse to the boundary, the uniform conormal energy estimates are established for the solutions to compressible MHD equations with respect to small viscosity coefficients. As a direct consequence, we proved the inviscid limit of solutions from viscous MHD systems to the ideal MHD systems in L ∞ sense. It shows that the transverse magnetic field can prevent the boundary layers from occurring in some physical regime.

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Boundary layer problems for the two-dimensional compressible Navier–Stokes equations

Cited by 19 publications

References 9 publications

Local-in-time well-posedness for compressible MHD boundary layer

Local-in-time well-posedness for compressible MHD boundary layer

Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow

Uniform regularity estimates and invisicid limit for the compressible non-resistive magnetohydrodynamics system

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