On the low regularity of the modified Korteweg-de Vries equation with a dissipative term

DOI10.1016/j.jde.2007.05.030zbMath1125.35080OpenAlexW2088992362MaRDI QIDQ996241

Junfeng Li, Chen, Wengu

Publication date: 13 September 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.05.030

zbMATH Keywords

Sobolev spacesCauchy problemwell-posednessill-posednessdissipative mKdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Ill-posed problems for PDEs (35R25) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05)

Related Items (5)

Analysis of 2 + 1 diffusive–dispersive PDE arising in river braiding ⋮ Global well-posedness and inviscid limit for the modified Korteweg-de Vries-Burgers equation ⋮ On ill-posedness for the generalized BBM equation ⋮ On the well-posedness of higher order viscous Burgers' equations ⋮ On the low regularity of the fifth order Kadomtsev-Petviashvili I equation

Cites Work

• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• The initial-value problem for the generalized Burger's equation
• Generalized Strichartz inequalities for the wave equation
• The dissipation of nonlinear dispersive waves: the case of asymptotically weak nonlinearity
• The Cauchy problem for dissipative Korteweg de Vries equations in Sobolev spaces of negative order
• A bilinear estimate with applications to the KdV equation
• Nonuniqueness and Uniqueness in the Initial-Value Problem for Burgers’ Equation
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