Browsing NTNU Open by Author "Grunert, Katrin"
Now showing items 1-13 of 13
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A Lagrangian view on complete integrability of the conservative Camassa– Holm flow
Eckhardt, Jonathan; Grunert, Katrin (Journal article; Peer reviewed, 2017)We show how the change from Eulerian to Lagrangian coordinates for the two-component Camassa–Holm system can be understood in terms of certain reparametrizations of the underlying isospectral problem. The respective ... -
A Lipschitz metric for the Hunter-Saxton equation
Carrillo, José A; Grunert, Katrin; Holden, Helge (Journal article; Peer reviewed, 2019)We analyze stability of conservative solutions of the Cauchy problem on the line for the (integrated) Hunter–Saxton (HS) equation. Generically, the solutions of the HS equation develop singularities with steep gradients ... -
A Lipschitz metric for the Hunter–Saxton equation
Antonio Carrillo, Jose; Grunert, Katrin; Holden, Helge (Journal article; Peer reviewed, 2019)We analyze stability of conservative solutions of the Cauchy problem on the line for the (integrated) Hunter–Saxton (HS) equation. Generically, the solutions of the HS equation develop singularities with steep gradients ... -
A continuous interpolation between conservative and dissipative solutions
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Peer reviewed; Journal article, 2015)We introduce a novel solution concept, denoted -dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system ... -
A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Peer reviewed; Journal article, 2015)We introduce a novel solution concept, denotedα-dissipative solutions, that provides a continuousinterpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system ... -
Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system
Grunert, Katrin; Nordli, Anders Samuelsen (Journal article, 2018)We establish the concept of α-dissipative solutions for the two-component Hunter–Saxton system under the assumption that either α(x)=1 or 0≤α(x)<1 for all x∈R. Furthermore, we investigate the Lipschitz stability of solutions ... -
Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Journal article, 2014)We show the existence of a global weak dissipative solution of the Cauchy problem for the two-component Camassa–Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second ... -
On the Burgers–Poisson equation
Grunert, Katrin; Nguyen, Khai Tien (Journal article, 2016)In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L 1 (R). In addition an Oleinik type estimate is established and some criteria on local ... -
On the Equivalence of Eulerian and Lagrangian Variables for the Two-Component Camassa–Holm System
Grunert, Katrin; Holden, Helge; Grasmair, Markus (Chapter, 2018)The Camassa–Holm equation and its two-component Camassa–Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the ... -
On the two-component Hunter–Saxton system
Nordli, Anders (Doctoral theses at NTNU;2017:146, Doctoral thesis, 2017)In 1991 Hunter and Saxton introduced a novel equation related to the dynamics of liquid crystals. The equation exhibited startling properties, among them wave breaking in finite time. Here we study the effects of ... -
Solutions of the Camassa-Holm equation with accumulating breaking times
Grunert, Katrin (Journal article, 2016)We present two initial profiles to the Camassa–Holm equation which yield solutions with accumulating breaking times -
Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system
Raynaud, Xavier; Grunert, Katrin (Chapter, 2018)Compared with the two-component Camassa–Holm system, the modified two-component Camassa–Holm system introduces a regularized density which makes possible the existence of solutions of lower regularity, and in particular ... -
The general peakon-antipeakon solution for the Camassa-Holm equation
Grunert, Katrin; Holden, Helge (Journal article; Peer reviewed, 2016)We compute explicitly the peakon-antipeakon solution of the Camassa– Holm equation ut − utxx + 3uux − 2uxuxx − uuxxx = 0 in the non-symmetric and α-dissipative case. The solution experiences wave breaking in finite time, ...