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Abstract
We consider a twodimensional, twolayer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or difference in density between the two layers, and the flow is inviscid. Unlike in previous studies, we consider solutions which are localised perturbations rather than periodic or quasiperiodic perturbations of a background shear flow. We rigorously construct a curve of exact solutions and give the leading order terms in an asymptotic expansion. We also give a thorough qualitative description of the fluid particle paths, which can include stagnation points, critical layers, and streamlines which meet the boundary.
Original language  English 

Pages (fromto)  376422 
Number of pages  47 
Journal  Journal of Differential Equations 
Volume  400 
Early online date  3 May 2024 
DOIs  
Publication status  Epub ahead of print  3 May 2024 
Data Availability Statement
No data was used for the research described in the article.Acknowledgements
We also thank the anonymous referee for their careful reading and useful comments.Keywords
 math.AP
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 1 Finished

Derivation of kinetic equation: From Newton to Boltzmann via trees
1/10/20 → 31/03/24
Project: UK charity