Basic Conservation Laws of the System of Equations of Two-Dimensional Shallow Water over an Uneven Bottom in the Lagrangian Variables
https://doi.org/10.1134/S2304487X19030039
Abstract
Systems of equations of two-dimensional shallow water over an uneven bottom have been considered in both the Eulerian and Lagrangian variables. An intermediate system of equations has been introduced. Its solutions are simultaneously solutions of the system of equations of two-dimensional shallow water in the Eulerian variables and implicit solutions of the system of equations of two-dimensional shallow water in the Lagrangian variables. All basic hydrodynamic conservation laws of the intermediate system of equations have been found without using symmetries. A relationship has been obtained between the conservation laws of the intermediate system of equations and the system of equations of two-dimensional shallow water in the Lagrangian variables. The basic hydrodynamic conservation laws of the intermediate system of equations have been used to construct the basic conservation laws of the first order for the system of equations of two-dimensional shallow water in the Lagrangian variables.
Supporting agencies: The work was carried out with partial financial supported by the RFBR grant 18-01-00890 and the Foundation development of theoretical physics and mathematics ”BASIS” (scholarship holder K. P. Druzhkov)
About the Authors
A. V. Aksenov
Moscow State University; Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
119991
125047
115409
Moscow
K. P. Druzhkov
Moscow State University; Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; Moscow Institute of Physics and Technology (State University)
Russian Federation
Russian Federation
119991
125047
141701
Moscow
Moscow region
Dolgoprudnyi
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Review
For citations:
Aksenov A.V., Druzhkov K.P. Basic Conservation Laws of the System of Equations of Two-Dimensional Shallow Water over an Uneven Bottom in the Lagrangian Variables. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2019;8(3):248- 252. (In Russ.) https://doi.org/10.1134/S2304487X19030039
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