Korteweg–de Vries–Burgers system in $\mathbb{R}^N$

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Tomasz Dlotko, Maria B. Kania, Shan Ma

Published: 14 Mar 2014, Last Modified: 18 Jan 2026OpenReview Archive Direct UploadEveryoneCC BY-NC-ND 4.0
Abstract: We study Cauchy problem in $\mathbb{R}^N$ for the Korteweg–de Vries–Burgers system. Parabolic regularization technique is used to prove its global in time solvability. The regularization effect of the Laplacian term is observed for the viscous solutions constructed in the paper. Asymptotic behavior of weak solutions is discussed next in the language of the global attractors.