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- W2950596561 abstract "We study the Cauchy problem for the modified KdV equation for data u_0 in the space ^H^r_s defined by the norm ||u_0||_{^H^r_s}:=|| ^s u^_0||_{L^r'_xi}. Local well-posedness of this problem is established in the parameter range 2>=r>1, s>=1/2-1/2r, so the case (s,r)=(0,1), which is critical in view of scaling considerations is almost reached. To show this result, we use an appropriate variant of the Fourier restriction norm method as well as bi- and trilinear estimates for solutions of the Airy equation." @default.
- W2950596561 created "2019-06-27" @default.
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- W2950596561 date "2007-03-01" @default.
- W2950596561 modified "2023-09-27" @default.
- W2950596561 title "Local well-posedness for the modified KdV equation in almost critical ^H^r_s-spaces" @default.
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