Browsing NTNU Open by Author "Grunert, Katrin"
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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 twocomponent Camassa–Holm system can be understood in terms of certain reparametrizations of the underlying isospectral problem. The respective ... 
A Lipschitz metric for the HunterSaxton 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 twocomponent Camassa–Holm system ... 
A continuous interpolation between conservative and dissipative solutions for the twocomponent CamassaHolm system
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Peer reviewed; Journal article, 2015)We introduce a novel solution concept, denotedαdissipative solutions, that provides a continuousinterpolation between conservative and dissipative solutions of the Cauchy problem for the twocomponent Camassa–Holm system ... 
Discretizations of Wave Equations and Applications of Variational Principles
Galtung, Sondre Tesdal (Doctoral theses at NTNU;2020:331, Doctoral thesis, 2020) 
Existence and Lipschitz stability for αdissipative solutions of the twocomponent Hunter–Saxton system
Grunert, Katrin; Nordli, Anders Samuelsen (Journal article, 2018)We establish the concept of αdissipative solutions for the twocomponent 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 twocomponent CamassaHolm 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 twocomponent Camassa–Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second ... 
A Lipschitz metric for the CamassaHolm equation
Antonio Carrillo, José; Grunert, Katrin; Holden, Helge (Peer reviewed; Journal article, 2020)We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving ... 
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 BurgersPoisson 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 TwoComponent Camassa–Holm System
Grunert, Katrin; Holden, Helge; Grasmair, Markus (Chapter, 2018)The Camassa–Holm equation and its twocomponent 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 twocomponent 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 ... 
A Regularized System for the Nonlinear Variational Wave Equation
Reigstad, Audun (Doctoral theses at NTNU;2021:21, Doctoral thesis, 2021) 
Solutions of the CamassaHolm 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 twocomponent CamassaHolm system
Raynaud, Xavier; Grunert, Katrin (Chapter, 2018)Compared with the twocomponent Camassa–Holm system, the modified twocomponent Camassa–Holm system introduces a regularized density which makes possible the existence of solutions of lower regularity, and in particular ... 
The general peakonantipeakon solution for the CamassaHolm equation
Grunert, Katrin; Holden, Helge (Journal article; Peer reviewed, 2016)We compute explicitly the peakonantipeakon solution of the Camassa– Holm equation ut − utxx + 3uux − 2uxuxx − uuxxx = 0 in the nonsymmetric and αdissipative case. The solution experiences wave breaking in finite time, ...