Existence results for viscous polytropic fluids with vacuum
Yonggeun Cho,Hyunseok Kim +1 more
253
TL;DR: In this paper, the authors considered the Navier-Stokes equations for viscous polytropic fluids with nonnegative thermal conductivity and proved the existence of unique local strong solutions for all initial data satisfying some compatibility condition.
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About: This article is published in Journal of Differential Equations. The article was published on 15 Sep 2006. and is currently open access. The article focuses on the topics: Polytropic process & Bounded function.
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Citations
On classical solutions of the compressible magnetohydrodynamic equations with vacuum
TL;DR: It is proved that the L^\infty$ norm of the deformation tensor of velocity gradients controls the possible blow-up for classical (or strong) solutions, which means that if a solution of the compressible MHD equations is initially regular and loses its regularity at some later time, then the formation of singularity must be caused by the losing the bound of the deformtion tensor as the critical time approches.
Blow-up criteria for a fluid dynamical model arising in astrophysics
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TL;DR: The paper deals with the existence of local strong solution for a fluid dynamical model arising in astrophysics and obtains blow-up criteria in terms of the velocity gradient, mass fraction gradient and temperature.
Global existence of the radially symmetric solutions of the Navier–Stokes equations for the isentropic compressible fluids
Hi Jun Choe,Hyunseok Kim +1 more
TL;DR: In this article, the authors studied the isentropic compressible Navier-Stokes equations with radially symmetric data in an annular domain and proved the global existence and regularity results on the radially-symmetric weak solutions with non-negative bounded densities.
On Blowup of Classical Solutions to the Compressible Navier-Stokes Equations
Zhouping Xin,Wei Yan +1 more
TL;DR: In this paper, the authors studied the finite time blow up of smooth solutions to the Navier-Stokes system when the initial data contain vacuums and showed that any classical solutions of viscous compressible fluids without heat conduction will blow up in finite time, as long as the initial dataset has an isolated mass group satisfying some suitable conditions.
Local Well-Posedness of Strong Solutions to the Three-Dimensional Compressible Primitive Equations
TL;DR: In this paper, the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics has been established, and it is shown that strong solutions exist, are unique, and depend continuously on the initial data.
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