Conservation Laws and Nonlocally Related Systems of Two-Dimensional Boundary Layer Models
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and
Abstract
Local conservation laws, potential systems, and nonlocal conservation laws are systematically computed for three-equilibrium two-component boundary layer models that describe different physical situations: a plate flow, a flow parallel to the axis of a circular cylinder, and a radial jet striking a planar wall. First, local conservation laws of each model are computed using the direct method. For each of the three boundary layer models, two local conservation laws are found. The corresponding potential variables are introduced, and nonlocally related potential systems and subsystems are formed. Then nonlocal conservation laws are sought, arising as local conservation laws of nonlocally related systems. For each of the three physical models, similar nonlocal conservation laws arise. Further nonlocal variables that lead to further potential systems are considered. Trees of nonlocally related systems are constructed; their structure coincides for all three models. The three boundary layer models considered in this work provide rich and interesting examples of the construction of trees of nonlocally related systems. In particular, the trees involve spectral potential systems depending on a parameter; these spectral potential systems lead to nonlocal conservation laws. Moreover, potential variables that are not locally related on solution sets of some potential systems become local functions of each other on solution sets of other systems. The point symmetry analysis shows that the plate and radial jet flow models possess infinite-dimensional Lie algebras of point symmetries, whereas the Lie algebra of point symmetries for the cylinder flow model is three-dimensional. The computation of nonlocal symmetries reveals none that arise for the original model equations, which is common for partial differential equations (PDE) systems without constitutive parameters or functions, but does reveal nonlocal symmetries for some nonlocally related PDE systems.
Acknowledgments
A.C. is grateful to the NSERC of Canada for research support through the Discovery grant program. R.N. is thankful to the Lahore School Of Economics for travel funding.
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Articles in the same Issue
- Frontmatter
- Ultrasonic Investigations on Polonides of Ba, Ca, and Pb
- The DFT Calculations of Structures and EPR Parameters for the Dinuclear Paddle-Wheel Copper(II) Complex {Cu2(μ2-O2CCH3)4}(OCNH2CH3) as Powder or Single Crystal
- Characteristics of Polarisation in the Ramsauer–Townsend Minima in Strongly Coupled Semiclassic Plasmas
- Streaming Jeans-Alfvén Instability in Quantum Magnetoplasmas
- Research for Coupled van der Pol Systems with Parametric Excitation and Its Application
- Interaction of Three Interfacial Cracks between an Orthotropic Half-Plane Bonded to a Dissimilar Orthotropic Layer with Punch
- Conservation Laws and Nonlocally Related Systems of Two-Dimensional Boundary Layer Models
- Localised Nonlinear Waves in the Three-Component Coupled Hirota Equations
- Nonlinear Stage of Modulation Instability for a Fifth-Order Nonlinear Schrödinger Equation
