论文信息 - Formation of singularities in three-dimensional compressible fluids

Formation of singularities in three-dimensional compressible fluids

Presented are several results on the formation of singularities in solutions to the three-dimensional Euler equations for a polytropic, ideal fluid under various assumptions on the initial data. In particular, it is shown that a localized fluid which is initially compressed and outgoing, on average, will develop singularities regardless of the size of the initial disturbance.

Thomas C. Sideris | T. Sideris

[1] T. Sideris. Formation of singularities in solutions to nonlinear hyperbolic equations , 1984 .

[2] Fritz John,et al. Formation of singularities in one‐dimensional nonlinear wave propagation , 1974 .

[3] Richard Courant,et al. Supersonic Flow And Shock Waves , 1948 .

[4] Tosio Kato,et al. The Cauchy problem for quasi-linear symmetric hyperbolic systems , 1975 .

[5] Peter D. Lax,et al. Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations , 1964 .

[6] A. Majda,et al. Compressible and incompressible fluids , 1982 .

[7] Thomas C. Sideris,et al. Global behavior of solutions to nonlinear wave equations , 1981 .

[8] Tai-Ping Liu. Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations , 1979 .

[9] Andrew J. Majda,et al. Formation of singularities for wave equations including the nonlinear vibrating string , 1980 .