Using the machinery of Lie-group analysis several equations arising in fluid mechanics are studied. In particular, the Burgers' equation, the KdV equation, the Hopf equation, the two-dimensional KdV equation and the Lin-Tsien equation are analyzed. In all cases the particular group includes arbitrary functions of time which permit the transformation of time-dependent equations into the corresponding time-independent ones. Infinitely many time-dependent solutions are associated with each steady solution. Some solutions are constructed.
Ames, W.F., NUCCI, M.C. (1986). Analysis of fluid equations by group methods. JOURNAL OF ENGINEERING MATHEMATICS, 20(2), 181-187 [10.1007/BF00042776].
Analysis of fluid equations by group methods
NUCCI, Maria Clara
1986
Abstract
Using the machinery of Lie-group analysis several equations arising in fluid mechanics are studied. In particular, the Burgers' equation, the KdV equation, the Hopf equation, the two-dimensional KdV equation and the Lin-Tsien equation are analyzed. In all cases the particular group includes arbitrary functions of time which permit the transformation of time-dependent equations into the corresponding time-independent ones. Infinitely many time-dependent solutions are associated with each steady solution. Some solutions are constructed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
