On the low regularity of the Korteweg-de Vries-Burgers equation

By Luc Molinet, Francis Ribaud. 2002

118 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7ae2d52cb4aae0a6f5f2fc78c8e7a6bedaee5783

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Citations in the corpus

Global well posedness and inviscid limit for the Korteweg-de Vries-Burgers equation (2008, methodology): “3 [6], we can show that ‖ψ(t)W ǫ (t)φ‖X1/2,s,α.”
The Initial-Boundary Value Problem for the Korteweg–de Vries Equation (2005, background): “or (1) and (2) when s<−3 4 . Interestingly, [BSZ05] have announced a LWP result for (5) for s>−1 by considering the equation solved by u(x,t)e−xand working with the solution constructed on R by [MR02]. Note that the trace map φ→ φ(0) is well-deﬁned on Hs(R+) when s> 1 2 . If s>1 2 , then”
A non-homogeneous boundary-value problem for the Korteweg–de Vries equation posed on a finite domain II (2003, background): “In addition, Molinet and Ribaud [35] showed that the pure initial-value problem ut + uux + uxxx − uxx = 0, −∞ < x < ∞, t > 0, u(x,0) = ψ(x), −∞ < x < ∞, } (1.6) for the KdV–Burgers equation is well-posed in the space Hs(R) for s > −1 and is ill-posed when s −1 in the sense that the corresponding s”
Improvement of the energy method for strongly non resonant dispersive equations and applications (2014, unknown): “We think that it could be dropped by replacing, in some estimates, the dispersive Bourgain’s spaces by dispersive-dissipative Bourgain’s spaces that were first introduced in [22].”
Global well-posedness of Korteweg-de Vries equation in H^-3/4 (R) (2008, methodology): “In view of this, we study instead the bilinear estimates in l1-type Xs,b space F s inspired by our work [7].”
Non-homogeneous boundary value problems for the Korteweg–de Vries and the Korteweg–de Vries–Burgers equations in a quarter plane (2008, methodology): “(3.17) When −1 s 0, Molinet and Ribaud [47] showed that the IVP for the KdV–Burgers equation is also globally well-posed in the space Hs( ) by taking the advantage of the dissipative term −uxx .”