Radu Dascaliuc 2003 Nonlinearity 16 1945 doi:10.1088/0951-7715/16/6/304
Radu Dascaliuc
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Burgers' model for turbulence consists of a PDE coupled with a nonlocal ODE. We study the behaviour, backward in time, of its solutions, which turns out to be quite different from the behaviour of the solutions of the space periodic two-dimensional Navier–Stokes equations (Constantin P, Foias C, Kukavica I and Majda A 1997 Dirichlet quotients and 2-D periodic Navier–Stokes equations J. Math. Pure Appl. 76 125–53) and space periodic one-dimensional Kuramoto–Sivashinsky equation (Kukavica I 1992 On the behavior of the solutions of the Kuramoto–Sivashinsky equations for negative time J. Math. Anal. Appl. 166 601–6).
02.30.Jr Partial differential equations
35Q35 Other equations arising in fluid mechanics
35B40 Asymptotic behavior of solutions
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
Issue 6 (November 2003)
Received 14 January 2003, in final form 23 June 2003
Published 19 August 2003
Radu Dascaliuc 2003 Nonlinearity 16 1945
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