Abstract
Assertions of the type of Lagrange's theorem are presented for three new classes of flows of an ideal incompressible liquid. The rest states of a liquid which is inhomogeneous with respect to its density (continuously stratified) and located in an external field of mass forces comprise the first class. Certain whirling (rotating) flows of a liquid which is homogeneous with respect to its density belong to the second and third classes. Unlike the situations which have been studied previously, flows belonging to the second and third classes are not states of relative or absolute rest and do not possess free boundaries. At the same time the formulations and proofs of the assertions are practically repeats of one another for all three cases. The question of the existence of an analogue of Lagrange's theorem in hydrodynamics has been studied in a number of papers (/1-4/, etc.).
| Original language | English |
|---|---|
| Pages (from-to) | 559-564 |
| Number of pages | 6 |
| Journal | Journal of Applied Mathematics and Mechanics |
| Volume | 50 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1986 |
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ASJC Scopus subject areas
- Modelling and Simulation
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics
Cite this
Analogues of the lagrange theorem in the hydrodynamics of whirling and stratified liquids. / Vladimirov, V. A.
In: Journal of Applied Mathematics and Mechanics, Vol. 50, No. 5, 1986, p. 559-564.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analogues of the lagrange theorem in the hydrodynamics of whirling and stratified liquids
AU - Vladimirov, V. A.
PY - 1986
Y1 - 1986
N2 - Assertions of the type of Lagrange's theorem are presented for three new classes of flows of an ideal incompressible liquid. The rest states of a liquid which is inhomogeneous with respect to its density (continuously stratified) and located in an external field of mass forces comprise the first class. Certain whirling (rotating) flows of a liquid which is homogeneous with respect to its density belong to the second and third classes. Unlike the situations which have been studied previously, flows belonging to the second and third classes are not states of relative or absolute rest and do not possess free boundaries. At the same time the formulations and proofs of the assertions are practically repeats of one another for all three cases. The question of the existence of an analogue of Lagrange's theorem in hydrodynamics has been studied in a number of papers (/1-4/, etc.).
AB - Assertions of the type of Lagrange's theorem are presented for three new classes of flows of an ideal incompressible liquid. The rest states of a liquid which is inhomogeneous with respect to its density (continuously stratified) and located in an external field of mass forces comprise the first class. Certain whirling (rotating) flows of a liquid which is homogeneous with respect to its density belong to the second and third classes. Unlike the situations which have been studied previously, flows belonging to the second and third classes are not states of relative or absolute rest and do not possess free boundaries. At the same time the formulations and proofs of the assertions are practically repeats of one another for all three cases. The question of the existence of an analogue of Lagrange's theorem in hydrodynamics has been studied in a number of papers (/1-4/, etc.).
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U2 - 10.1016/0021-8928(86)90028-6
DO - 10.1016/0021-8928(86)90028-6
M3 - Article
VL - 50
SP - 559
EP - 564
JO - Journal of Applied Mathematics and Mechanics
JF - Journal of Applied Mathematics and Mechanics
SN - 0021-8928
IS - 5
ER -