Global existence versus blow‐up results for one dimensional compressible Navier–Stokes equations with Maxwell's law
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DOI: 10.1002/mana.201700418
Abstract: We consider one dimensional isentropic compressible Navier–Stokes equations with constitutive relation of Maxwell's law instead of Newtonion law. For this new model, we show that for small initial data, a unique smooth solution exists globally… read more here.
Keywords: compressible navier; stokes equations; one dimensional; maxwell law ... See more keywords
Existence and zero-electron-mass limit of strong solutions to the stationary compressible Navier-Stokes-Poisson equation with large external force
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DOI: 10.1002/mma.4634
Abstract: In this study, we consider a viscous compressible model of plasma and semiconductors, which is expressed as a compressible Navier-Stokes-Poisson equation. We prove that there exists a strong solution to the boundary value problem of… read more here.
Keywords: poisson equation; compressible navier; stokes poisson; electron ... See more keywords
Slip Boundary Conditions for the Compressible Navier–Stokes Equations
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DOI: 10.1007/s10955-017-1886-8
Abstract: The slip boundary conditions for the compressible Navier–Stokes equations are derived systematically from the Boltzmann equation on the basis of the Chapman–Enskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent… read more here.
Keywords: compressible navier; slip boundary; boundary conditions; stokes equations ... See more keywords
On scaling invariance and type-I singularities for the compressible Navier-Stokes equations
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DOI: 10.1007/s11425-018-9363-1
Abstract: We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-I singularities of solutions with $$\mathop {\lim \sup }\limits_{t \nearrow T} |div(t,x)|(T - t) \leqslant \kappa $$limsupt↗T|div(t,x)|(T−t)≤κ can… read more here.
Keywords: compressible navier; invariance; type singularities; stokes equations ... See more keywords
Global well-posedness and time-decay estimates for compressible Navier-Stokes equations with reaction diffusion
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DOI: 10.1007/s11425-020-1779-7
Abstract: We consider the full compressible Navier-Stokes equations with reaction diffusion. A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a neighborhood of… read more here.
Keywords: compressible navier; stokes equations; time; time decay ... See more keywords
A sharp time-weighted inequality for the compressible Navier–Stokes–Poisson system in the critical L framework
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DOI: 10.1016/j.jde.2018.11.005
Abstract: Abstract The compressible Navier–Stokes–Poisson system takes the form of usual Navier–Stokes equations coupled with the self-consistent Poisson equation, which is used to simulate the transport of charged particles under the electrostatic potential force. In this… read more here.
Keywords: time; poisson system; sharp time; compressible navier ... See more keywords
On a simplified compressible Navier-Stokes equations with temperature-dependent viscosity
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DOI: 10.1016/j.jde.2019.09.023
Abstract: Abstract We consider a simplified compressible Navier-Stokes equations with cylindrical symmetry when viscosity coefficient λ and heat conductivity coefficient κ depend on temperature. We obtain global existence of strong solution and vanishing shear viscosity limit… read more here.
Keywords: viscosity; compressible navier; stokes equations; simplified compressible ... See more keywords
Optimal decay rates of isentropic compressible Navier-Stokes equations with discontinuous initial data
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DOI: 10.1016/j.jde.2020.06.021
Abstract: Abstract The global-in-time solutions with discontinuous initial data, when the density has no regularity, are constructed in [10] , [11] , [12] for the isentropic compressible Navier-Stokes equations in multi-dimensional spaces. The time decay rates… read more here.
Keywords: compressible navier; isentropic compressible; decay rates; discontinuous initial ... See more keywords
Global solutions to compressible Navier-Stokes-Poisson and Euler-Poisson equations of plasma on exterior domains
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DOI: 10.1016/j.jde.2020.07.005
Abstract: Abstract The initial boundary value problems for compressible Navier-Stokes-Poisson and Euler-Poisson equations of plasma are considered on exterior domains in this paper. With the radial symmetry assumption, the global existence of solutions to compressible Navier-Stokes-Poisson… read more here.
Keywords: compressible navier; stokes poisson; poisson euler; poisson equations ... See more keywords
Nonlinearly exponential stability for the compressible Navier-Stokes equations with temperature-dependent transport coefficients
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DOI: 10.1016/j.jde.2021.03.044
Abstract: Abstract This paper is concerned with an initial and boundary value problem of the compressible Navier-Stokes equations for one-dimensional viscous and heat-conducting ideal polytropic fluids with temperature-dependent transport coefficients. In the case when the viscosity… read more here.
Keywords: stokes equations; dependent transport; navier stokes; compressible navier ... See more keywords
Vanishing dissipation limit to the planar rarefaction wave for the three-dimensional compressible Navier-Stokes-Fourier equations
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DOI: 10.1016/j.jfa.2022.109499
Abstract: Abstract. We study the vanishing dissipation limit of the three-dimensional (3D) compressible Navier-Stokes-Fourier equations to the corresponding 3D full Euler equations. Our results are twofold. First, we prove that the 3D compressible Navier-Stokes-Fourier equations admit… read more here.
Keywords: fourier equations; dissipation; stokes fourier; compressible navier ... See more keywords