Analysis of fluid equations by group methods. (English) Zbl 0628.35004
For certain equations arising in fluid mechanics, namely the Navier- Stokes equation, Burger equation, Korteweg-de Vries equation, 2d- Korteweg-de Vries equation and Lin Tsien’s equation, the authors give the full underlying Lie group. Using these Lie groups they construct explicit (and special) solutions for some of the equations under consideration. (It is not always clear, which results are new and which are due to the authors.)
Reviewer: N.Jacob
MSC:
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 35Q30 | Navier-Stokes equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35C10 | Series solutions to PDEs |
Keywords:
fluid mechanics; Navier-Stokes equation; Burger equation; Korteweg-de Vries equation; Lin Tsien’s equation; Lie groupReferences:
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