On the ill-posedness of some canonical dispersive equations

2001/02/15 by Carlos E. Kenig, Gustavo Ponce, Luis Vega · 28 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Navier-Stokes equation solutions

paper · doi:10.1215/s0012-7094-01-10638-8

Abstract

We study the initial value problem (IVP) associated to some canonical dispersive equations. Our main concern is to establish the minimal regularity property required in the data which guarantees the local well-posedness of the problem. Measuring this regularity in the classical Sobolev spaces, we show ill-posedness results for Sobolev index above the value suggested by the scaling argument.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Nonlinear scalar field equations, II existence of infinitely many solutions

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