Global Well-Posedness for Dissipative Korteweg-de Vries Equations

Abstract

Abstract. This paper is devoted to the well-posedness for dissipative KdV equationsAn optimal bilinear estimate is obtained in Bourgain's type spaces, which provides global well-posedness in H s ðRÞ, s > À3=4 for a a 1=2 and s > À3=ð5 À 2aÞ for a > 1=2.

Global well-posedness and inviscid limit for the Korteweg–de Vries–Burgers equation

“…The notations used in this paper can be found in Section 2. 1 After the paper was finished, the authors have been informed that the same results in this part were also obtained by Stéphane Vento [13] using the similar method. Theorem 1.1.…”

Well-posedness and asymptotic behavior of the dissipative Ostrovsky equation

“…The following local existence is a consequence of Theorem 1.2 together with linear estimates of Section 2 (see the proof of Theorem 1.3 in [29]). .…”

“…One can see [18] to study a well-posedness result of (1.1) at the critical regularity. By working on suitable Bourgain-type spaces, equation (1.4) was proved in [12,29] to be globally well-posed in H s (R), s > s α,c , where…”

“…The global well-posedness will follow from Theorems 1.3 and 1.4 (see the proofs of Theorem 1.1 in [23] and Theorem 1.3 in [29]). Theorem 1.5.…”

Global well-posedness and inviscid limit for the modified Korteweg–de Vries–Burgers equation

“…Their result is sharp in the sense that the solution map of (1.2) fails to be C 2 smooth at origin if s < −1. Their result is generalized to the case 0 < α ≤ 1 by Vento [16], also by Guo and Wang [5] and found a critical wellposedness regularity s α = −3/4, 0 < α ≤ 1/2, −3/(5 − 2α), 1/2 < α ≤ 1.…”