Notes on the Incompressible Euler and Related Equations on R^N
Notes on the Incompressible Euler and Related Equations on R^N
摘要
The author reviews briefly some of the recent results on the blow-up problem for the incompressible Euler equations on RN,and also presents Liouville type theorems for the incompressible and compressible fluid equations.
基金
Project supported by KRF Grant (MOEHRD,Basic Research Promotion Fund)
参考文献17
-
1Dongho Chae.Nonexistence of Self-Similar Singularities for the 3D Incompressible Euler Equations[J].Communications in Mathematical Physics.2007(1)
-
2Dongho Chae.Nonexistence of asymptotically self-similar singularities in the Euler and the Navier–Stokes equations[J].Mathematische Annalen.2007(2)
-
3Diego Cordoba,Charles Fefferman.On the Collapse of Tubes Carried?by 3D Incompressible Flows[J].Communications in Mathematical Physics.2001(2)
-
4Judith R. Miller,Mike O’Leary,Maria Schonbek.Nonexistence of singular pseudo-self-similar solutions of the Navier–Stokes system[J].Mathematische Annalen.2001(4)
-
5Tai‐Peng Tsai.On Leray’s Self‐Similar Solutions of the Navier‐Stokes Equations Satisfying Local Energy Estimates[J].Archive for Rational Mechanics and Analysis.1998(1)
-
6J. T. Beale,T. Kato,A. Majda.Remarks on the breakdown of smooth solutions for the 3-D Euler equations[J].Communications in Mathematical Physics.1984(1)
-
7Jean Leray.Sur le mouvement d’un liquide visqueux emplissant l’espace[J].Acta Mathematica.1934(1)
-
8Bardos,C.,Titi,E.S.Euler equations of incompressible ideal uids[].RussMathSurv.2007
-
9da Veiga,H.B.Vorticity and smoothness in incompressible viscous ows(wave phenomena and asymptotic analysis)[].RIMS Kokyuroku.2003
-
10da Veiga,H.B.,Berselli,L.C.On the regularizing e ect of the vorticity direction in incompressible viscous ows[].DiIntEqs.2002
-
1王建田.一维可压缩Euler方程的渐近解[J].南京大学学报（数学半年刊）,1995,12(1):121-127.
-
2Maria Schonbek.NONEXISTENCE OF PSEUDO-SELF-SIMILAR SOLUTIONS TO INCOMPRESSIBLE EULER EQUATIONS[J].Acta Mathematica Scientia,2011,31(6):2305-2312.
-
3Zaihui GAN,Boling GUO.Compressible Limit of the Nonlinear Schrdinger Equation with Different-Degree Small Parameter Nonlinearities[J].Chinese Annals of Mathematics,Series B,2011,32(1):105-122.
-
4程晓晗,聂玉峰,封建湖,Luo Xiao-Yu,蔡力.Self-adjusting entropy-stable scheme for compressible Euler equations[J].Chinese Physics B,2015,24(2):16-22. 被引量：1
-
5朱旭生,熊显萍,傅湧.一维可压缩欧拉方程组解的爆破[J].华东交通大学学报,2009,26(2):111-114. 被引量：3
-
6熊显萍,朱旭生.带非线性阻尼项的欧拉方程初值问题经典解的爆破[J].贵州师范大学学报（自然科学版）,2011,29(3):97-99. 被引量：4
-
7高真圣,张培欣.二维等熵可压欧拉方程古典解的存在性(英文)[J].数学研究,2013,46(3):221-232.
-
8张新丽,张春凤.一维可压缩Euler方程经典解的破裂[J].菏泽学院学报,2006,28(2):12-15.
-
9朱春蓉,朱丹霞.可压缩欧拉方程在不变子空间中的精确解[J].工程数学学报,2016,33(3):279-286. 被引量：3
-
10梁之磊.可压缩欧拉方程解的blowup现象[J].厦门大学学报（自然科学版）,2012,51(4):657-659. 被引量：7
