An improved local well-posedness result for the modified KdV equation
By A. Gruenrock. 2003
113 citations recorded by the source corpus.
The Cauchy problem for the modified KdV equation is shown to be locally well posed for data u_0 in the space \hat(H^r_s) defined by the norm ||u_0||:=|| ^s \hat(u_0)||_L^r', provided 4/3 < r \le 2, s \ge 1/2 - 1/(2r). For r=2 this coincides with the best possible result on the H^s - scale due to Kenig, Ponce and Vega. The proof uses an appropriate variant of the Fourier restriction norm method and linear as well as bilinear estimates for the solutions of the Airy equation.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/7e090110760a6e907de60be000567f46a21eb668
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Long time behavior of solutions to the mKdV (2014, background): “Local well-posedness in non-L(2)-based spaces closer to the critical scaling has also been obtained [9, 10].”