Browsing NTNU Open by Author "Ehrnstrom, Mats"
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A note on the local wellposedness for the whitham equation
Ehrnstrom, Mats; Escher, Joachim; Pei, Long (Journal article; Peer reviewed, 2015)We prove local wellposedness for the Whitham equation in Hs, s>32s>32, for both solitary and periodic initial data. 
Classical wellposedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces
Ehrnstrom, Mats; Pei, Long (Journal article; Peer reviewed, 2018)For both localized and periodic initial data, we prove local existence in classical energy space Hs,s > 3 2 , for a class of dispersive equations ut +(n(u))x +Lux = 0 with nonlinearities of mild regularity. Our results are ... 
Enhanced existence time of solutions to the fractional Korteweg de Vries equation
Ehrnstrom, Mats; Wang, Yuexun (Peer reviewed; Journal article, 2019)We consider the fractional Korteweg–de Vries equation ut+ uux−D αux = 0 in the range of −1 < α < 1, α 6= 0. Using basic Fourier techniques in combination with the modified energy method we extend the existence time of ... 
Existence of a Highest Wave in a Fully Dispersive TwoWay Shallow Water Model
Ehrnstrom, Mats; Johnson, Mathew A; Claassen, Kyle M (Journal article; Peer reviewed, 2018)We consider the existence of periodic traveling waves in a bidirectional Whitham equation, combining the full twoway dispersion relation from the incompressible Euler equations with a canonical shallow water nonlinearity. ... 
On the Bifurcation Diagram of the Capillary–Gravity Whitham Equation
Ehrnstrom, Mats; Remonato, Filippo; Mæhlen, Ola Isaac Høgåsen; Johnson, Mathew A (Journal article, 2019)We study the bifurcation of periodic travelling waves of the capillary–gravity Whitham equation. This is a nonlinear pseudodifferential equation that combines the canonical shallow water nonlinearity with the exact ... 
On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
Ehrnstrom, Mats; Wahlén, Erik (Peer reviewed; Journal article, 2019)We consider the Whitham equation ut + 2uux + Lux = 0, where L is the nonlocal Fourier multiplier operator given by the symbol m(ξ) = p tanh ξ/ξ. G. B. Whitham conjectured that for this equation there would be a highest, ... 
Smallamplitude fully localised solitary waves for the fulldispersion KadomtsevPetviashvili equation
Ehrnstrom, Mats; Groves, Mark D (Journal article; Peer reviewed, 2018)The KPI equation arises as a weakly nonlinear model equation for gravitycapillary waves with strong surface tension (Bond number ). This equation admits—as an explicit solution—a 'fully localised' or 'lump' solitary ... 
Symmetric solutions of evolutionary partial differential equations
Ehrnstrom, Mats; Bruell, Gabriele; Pei, Long; Geier, Anna (Journal article; Peer reviewed, 2017)We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are ... 
Symmetry and decay of traveling wave solutions to the Whitham equation
Ehrnstrom, Mats; Brüll, Gabriele; Pei, Long (Journal article, 2017)This paper is concerned with decay and symmetry properties of solitarywave solutions to a nonlocal shallowwater wave model. An exponential decay result for supercritical solitarywave solutions is given. Moreover, it is ...