三维空间中带非线性阻尼项的等熵欧拉方程组轴对称解的爆破
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摘要
研究了三维空间中带非线性阻尼项的可压缩等熵欧拉方程组Dirichlet初边值问题.采用泛函方法,定义几种不同的泛函,当初始速度足够大时分别得到了经典解在某一时间内必定爆破的结论.由于出现了非线性阻尼项,较之线性阻尼的情形,经典解爆破的难度随之增加.
The blowup of axisymmetric solutions for the initial-boundary value problem of the compressible isentropic Euler equations with nonlinear damping in R3 is investigated in this paper.We show by functional methods that classical solutions will blow up before a certain time under the assumption that the functional associated with the initial velocity is sufficiently large.Compared to the linear damping case,the damping increased the difficulty of the blowup of the classical solution.
The blowup of axisymmetric solutions for the initial-boundary value problem of the compressible isentropic Euler equations with nonlinear damping in R3 is investigated in this paper.We show by functional methods that classical solutions will blow up before a certain time under the assumption that the functional associated with the initial velocity is sufficiently large.Compared to the linear damping case,the damping increased the difficulty of the blowup of the classical solution.
引文
[1]Thomas C.Sideris,Becca Thomases,Dehua Wang.Long time behavior of solutions to the 3D compressible Euler equations with damping[J].Communications in Partial Differential Equations,2003,28(3):795-816.
[2]Wang W,Yang T.The pointwise estimates of solutions for Euler equations with damping in multidimensions[J].J Differential Equations,2001,173:410-450.
[3]Liu Y Q,Wang W.Well-posedness of the IBVP for 2-D Euler equations with damping[J].J Differential Equations,2008,245:2477-2503.
[4]Zhu X S.The Global Solution Of Initial-Boundary Value Problem For Euler Equations With Damping[J].J of math,2004(4):370-374.
[5]朱长江,蒋咪娜.具有非线性阻尼项的-方程组非线性扩散波的-衰减率[J].中国科学A辑,2006,36(3):262-280.
[6]朱旭生,熊显萍,涂爱花.带非线性阻尼项的等熵欧拉方程组的整体解[J].武汉大学学报(理学版),2011,57(4):93-99.
[7]Sideris T.Formation of singularities in three-dimensional compressible fluids[J].Comm Math Phys,1985,101:475-485.
[8]Yin H,Qiu Q.The blowup of solutions for 3D axisymmetric compressible Euler equations[J].Nagoya Math J 1999,154:157-169.
[9]熊显萍,朱旭生.带非线性阻尼的等熵欧拉方程组正规解的爆破[J].西南大学学报(自然科学版),2014,36(3):71-76.
[10]Zhu X S,Tu A H.Blowup of the axisymmetric solutions for the IBVP of the isentropic Euler equations[J].Nonlinear Analysis:Theory,methods&:App;ications,2014,95:99-106.
[11]朱旭生,俞银晶,李翠.带阻尼项的三维等熵可压缩欧拉方程组轴对称解的爆破[J].厦门大学学报(自然科学版),2014,53(6):780-784.
[12]Li T,Wang D.Blowup phenomena of solutions to the Euler equations for compressible fluid flow[J].J Differential Equations,2006,221(1):91-101.
[2]Wang W,Yang T.The pointwise estimates of solutions for Euler equations with damping in multidimensions[J].J Differential Equations,2001,173:410-450.
[3]Liu Y Q,Wang W.Well-posedness of the IBVP for 2-D Euler equations with damping[J].J Differential Equations,2008,245:2477-2503.
[4]Zhu X S.The Global Solution Of Initial-Boundary Value Problem For Euler Equations With Damping[J].J of math,2004(4):370-374.
[5]朱长江,蒋咪娜.具有非线性阻尼项的-方程组非线性扩散波的-衰减率[J].中国科学A辑,2006,36(3):262-280.
[6]朱旭生,熊显萍,涂爱花.带非线性阻尼项的等熵欧拉方程组的整体解[J].武汉大学学报(理学版),2011,57(4):93-99.
[7]Sideris T.Formation of singularities in three-dimensional compressible fluids[J].Comm Math Phys,1985,101:475-485.
[8]Yin H,Qiu Q.The blowup of solutions for 3D axisymmetric compressible Euler equations[J].Nagoya Math J 1999,154:157-169.
[9]熊显萍,朱旭生.带非线性阻尼的等熵欧拉方程组正规解的爆破[J].西南大学学报(自然科学版),2014,36(3):71-76.
[10]Zhu X S,Tu A H.Blowup of the axisymmetric solutions for the IBVP of the isentropic Euler equations[J].Nonlinear Analysis:Theory,methods&:App;ications,2014,95:99-106.
[11]朱旭生,俞银晶,李翠.带阻尼项的三维等熵可压缩欧拉方程组轴对称解的爆破[J].厦门大学学报(自然科学版),2014,53(6):780-784.
[12]Li T,Wang D.Blowup phenomena of solutions to the Euler equations for compressible fluid flow[J].J Differential Equations,2006,221(1):91-101.