Low regularity solutions of two fifth-order KdV type equations
نویسندگان
چکیده
The Kawahara and modified Kawahara equations are fifth-order KdV type equations and have been derived to model many physical phenomena such as gravitycapillary waves and magneto-sound propagation in plasmas. This paper establishes the local well-posedness of the initial-value problem for Kawahara equation in H(R) with s > − 4 and the local well-posedness for the modified Kawahara equation in H(R) with s ≥ − 4 . To prove these results, we derive a block estimate for the Kawahara equation through the [k;Z] multiplier norm method of Tao [14] and use this to obtain new bilinear and trilinear estimates in suitable Bourgain spaces. AMS (MOS) Numbers: 35Q53, 35B30, 76B45
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