Geodesic
A~possibility of realizing the~Landau--Hopf scenario in the~problem of tube oscillations under the~action of a~fluid flow
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 78-90

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We consider a boundary-value problem for a quasilinear partial differential equation describing tube oscillations under the action of a fluid flow. We show that the well-known Landau–Hopf scenario of transition to turbulence is realized in the considered evolution boundary-value problem with a suitable choice of the governing parameter. To study the problem, we use the theory of infinite-dimensional dynamical systems. In particular, we use the method of integral manifolds, normal forms, and also asymptotic methods of analysis.
Keywords: nonlinear evolution boundary-value problem, stability, invariant torus, asymptotic formula.
Mots-clés : bifurcation 
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     author = {A. N. Kulikov and D. A. Kulikov},
     title = {A~possibility of realizing {the~Landau--Hopf} scenario in the~problem of tube oscillations under the~action of a~fluid flow},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2020},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a5/}
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A. N. Kulikov; D. A. Kulikov. A~possibility of realizing the~Landau--Hopf scenario in the~problem of tube oscillations under the~action of a~fluid flow. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 78-90. http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a5/