On Formation of Singularity of Spherically Symmetric Nonbarotropic Flows

Type: Preprint

Publication Date: 2014-12-31

Citations: 10

Abstract

We study an initial boundary value problem on a ball for the heat-conductive system of compressible Navier-Stokes-Fourier equations, in particular, a criterion of breakdown of the classical solution. For smooth initial data away from vacuum, it is proved that the classical solution which is spherically symmetric loses its regularity in a finite time if and only if the {\bf density} {\it concentrates} or {\it vanishes} or the {\bf velocity} becomes unbounded around the center. One possible situation is that a vacuum ball appears around the center and the density may concentrate on the boundary of the vacuum ball simultaneously.

Locations

  • arXiv (Cornell University) - View - PDF

Similar Works

Action Title Year Authors
+ On formation of singularity of spherically symmetric nonbarotropic flows 2015 Xiangdi Huang
+ A CHARACTERIZATION ON BREAKDOWN OF SMOOTH SPHERICALLY SYMMETRIC SOLUTIONS OF THE ISENTROPIC SYSTEM OF COMPRESSIBLE NAVIERā€“STOKES EQUATIONS 2015 Xiangdi Huang
Akitaka Matsumura
+ Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum 2022 Yue Cao
Hao Li
Shengguo Zhu
+ Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball 2019 Dongfen Bian
Jinkai Li
+ Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball 2019 Dongfen Bian
Jinkai Li
+ PDF Chat Immediate Blowup of Entropy-Bounded Classical Solutions to the Vacuum Free Boundary Problem of Nonisentropic Compressible Navierā€“Stokes Equations 2023 Xin Liu
Yuan Yuan
+ PDF Chat On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity 2016 Xiangdi Huang
Zhouping Xin
+ Global spherically symmetric classical solution to the Navier-Stokes-Maxwell system with large initial data and vacuum 2014 Hong Guang
+ On formation of singularity to the 2D Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction 2017 Xin Zhong
+ On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity 2015 Xiangdi Huang
Zhouping Xin
+ PDF Chat Global well-posedness of the half space problem of the Navierā€“Stokes equations in critical function spaces of limiting case 2020 Tongkeun Chang
Bum Ja Jin
+ PDF Chat Singularity Formation for Radially Symmetric Expanding Wave of Compressible Euler Equations 2023 Hong Cai
Geng Chen
Tian-Yi Wang
+ PDF Chat Vacuum Behaviors around Rarefaction Waves to 1D Compressible Navier--Stokes Equations with Density-Dependent Viscosity 2013 Quansen Jiu
Yi Wang
Zhouping Xin
+ Vacuum behaviors around rarefaction waves to 1D compressible Navier-Stokes equations with density-dependent viscosity 2011 Quansen Jiu
Yi Wang
Zhouping Xin
+ Local Existence and Uniqueness of Strong Solutions to the Free Boundary Problem of the Full Compressible Navier--Stokes Equations in three dimensions 2019 Xin Liu
Yuan Yuan
+ Local well-posedness of the free boundary problem of the full compressible Navier-Stokes equations in 3D 2018 Xin Liu
Yuan Yuan
+ Immediate blowup of entropy-bounded classical solutions to the vacuum free boundary problem of non-isentropic compressible Navier--Stokes equations 2022 Xin Liu
Yuan Yuan
+ Existence of the stationary Navier-Stokes flow in $\mathbb{R}^2$ around a radial flow 2021 Yasunori Maekawa
Hiroyuki Tsurumi
+ Formation of Singularity for Compressible Euler Equations Outside a Ball in 3-D 2024 M. Li
Jinbo Geng
+ Global well-posedness of the half space problem of the Navier-Stokes equations in critical function spaces of limiting case 2020 Tongkeun Chang
Bum Ja Jin

Works Cited by This (20)

Action Title Year Authors
+ A CHARACTERIZATION ON BREAKDOWN OF SMOOTH SPHERICALLY SYMMETRIC SOLUTIONS OF THE ISENTROPIC SYSTEM OF COMPRESSIBLE NAVIERā€“STOKES EQUATIONS 2015 Xiangdi Huang
Akitaka Matsumura
+ PDF Chat The initial value problem for the equations of motion of viscous and heat-conductive gases 1980 Akitaka Matsumura
Takaaki Nishida
+ PDF Chat On Blowup of Classical Solutions to the Compressible Navier-Stokes Equations 2012 Zhouping Xin
Wei Yan
+ On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid 1995 Š’. Š. Š’Š°Š¹Š³Š°Š½Ń‚
A. V. Kazhikhov
+ PDF Chat A blow-up criterion for classical solutions to the compressible Navier-Stokes equations 2010 Xiangdi Huang
Zhouping Xin
+ PDF Chat Solvability of the initial-boundary-value problem for the equations of motion of a viscous compressible fluid 1980 V. A. Solonnikov
+ PDF Chat On the Cauchy problem for the system of fundamental equations describing the movement of compressible viscous fluid 1971 Nobutoshi Itaya
+ PDF Chat Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids 1983 Akitaka Matsumura
Takaaki Nishida
+ PDF Chat On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities 2006 Yonggeun Cho
Hyunseok Kim
+ Global existence of the radially symmetric solutions of the Navierā€“Stokes equations for the isentropic compressible fluids 2004 Hi Jun Choe
Hyunseok Kim