M M Vishik and S Friedlander 1993 Nonlinearity 6 231 doi:10.1088/0951-7715/6/2/005
M M Vishik and S Friedlander
Show affiliationsAn inverse scattering 'recipe' is presented for obtaining the solution of a Lagrangian formulation of the Euler equations governing the motion of an unbounded two-dimensional ideal fluid. This formulation is given in terms of a so-called Lax pair of operators. The scattering data are viewed as a delta -data in order to apply the approach for multidimensional inverse scattering. The operator of the Lax pair associated with the spectral problem is treated as a perturbation of the analogous problem for the Laplacian. It is shown that solutions to the direct and inverse problems exist when, in an appropriate sense, this perturbation is small. A particular example is discussed in which the initial velocity has the asymptotic structure of a point vortex. In this case the explicit integral equation is exhibited for the eigenfunctions from which the flow description can be reconstructed.
Issue 2 (March 1993)
M M Vishik and S Friedlander 1993 Nonlinearity 6 231
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