On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid

Вайгант, В. А.; Kazhikhov, A. V.

doi:10.1007/bf02106835

Cited by 203 publications

(257 citation statements)

References 7 publications

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“…Motivated by [10], where the authors proved the global existence of classical solutions to (1.1) for λ = ̺ β with β > 3, we shall prove in this paper that sup…”

Section: Introductionmentioning

confidence: 91%

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On the blow up criterion for the 2-D compressible Navier-Stokes equations

Ling-yu¹,

Wang²

2010

Czech Math J

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“…Motivated by [10], where the authors proved the global existence of classical solutions to (1.1) for λ = ̺ β with β > 3, we shall prove in this paper that sup…”

Section: Introductionmentioning

confidence: 91%

“…An estimate of higher derivatives of U is obtained by carrying out calculations similar to but easier than (15) and (16) in [10]: (2.14)…”

Section: Now We Note Thatmentioning

confidence: 99%

On the blow up criterion for the 2-D compressible Navier-Stokes equations

Ling-yu¹,

Wang²

2010

Czech Math J

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“…In recent years, the local or global (in time) solvability to the various initial boundary value problem for the Navier-Stokes equation for nonstationary compressible viscous fluid has been established by many authors (see, e.g. [16], [17], [18], [19], [25]). The most general results are…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Spatial Decay Bounds of Solutions to the Navier-Stokes Equations for Transient Compressible Viscous Flow

Lü¹,

Qiu²,

Cheng³

2011

Journal of the Korean Mathematical Society

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“…For related free boundary problems for isentropic fluids with density-dependent viscosity, see Liu-Xin-Yang [19], Luo-Xin-Yang [20], and the earlier references cited therein. Also see Lions [18] and Vaigant-Kazhikhov [32] for related references for multidimensional isentropic fluids.…”

Section: Introductionmentioning

confidence: 99%

Global Solutions to the Navier-Stokes Equations for Compressible Heat-Conducting Flow With Symmetry and Free Boundary

Kratka

2002

Communications in Partial Differential Equations

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Global solutions of the multidimensional Navier-Stokes equations for compressible heatconducting flow are constructed, with spherically symmetric initial data of large oscillation between a static solid core and a free boundary connected to a surrounding vacuum state. The free boundary connects the compressible heat-conducting fluids to the vacuum state with free normal stress and zero normal heat flux. The fluids are initially assumed to fill with a finite volume and zero density at the free boundary, and with bounded positive density and temperature between the solid core and the initial position of the free boundary. One of the main features of this problem is the singularity of solutions near the free boundary. Our approach is to combine an effective difference scheme to construct approximate solutions with the energy methods and the pointwise estimate techniques to deal with the singularity of solutions near the free boundary and to obtain the bounded estimates of the solutions and the free boundary as time evolves. The convergence of the difference scheme is established. It is also proved that no vacuum develops between the solid core and the free boundary, and the free boundary expands with finite speed.1991 Mathematics Subject Classification. Primary: 35D05, 76N10, 35R35, 65M12; Secondary: 65M06, 35B45, 76T99.

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On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid

Cited by 203 publications

References 7 publications

On the blow up criterion for the 2-D compressible Navier-Stokes equations

On the blow up criterion for the 2-D compressible Navier-Stokes equations

Spatial Decay Bounds of Solutions to the Navier-Stokes Equations for Transient Compressible Viscous Flow

Global Solutions to the Navier-Stokes Equations for Compressible Heat-Conducting Flow With Symmetry and Free Boundary

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