Blar i Institutt for matematiske fag på forfatter "Ehrnstrom, Mats"
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A note on the local well-posedness for the whitham equation
Ehrnstrom, Mats; Escher, Joachim; Pei, Long (Journal article; Peer reviewed, 2015)We prove local well-posedness for the Whitham equation in Hs, s>32s>32, for both solitary and periodic initial data. -
Classical well-posedness 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 ... -
A direct construction of a full family of Whitham solitary waves
Ehrnstrom, Mats; Nik, Katerina; Walker, Christoph (Peer reviewed; Journal article, 2022)Starting with the periodic waves earlier constructed for the gravity Whitham equation, we parameterise the solution curves through relative wave height, and use a limiting argument to obtain a full family of solitary waves. ... -
Enhanced existence time of solutions to evolution equations of Whitham type
Ehrnstrom, Mats; Wang, Yuexun (Peer reviewed; Journal article, 2022)We show that Whitham type equations , where is a general Fourier multiplier operator of order , , allow for small solutions to be extended beyond their ordinary existence time. The result is valid for a range of quadratic ... -
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 Two-Way 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 two-way dispersion relation from the incompressible Euler equations with a canonical shallow water nonlinearity. ... -
Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvilii equation
Ehrnstrom, Mats; Nilsson, Dag; Groves, Mark D (Peer reviewed; Journal article, 2022)We prove the existence of small-amplitude modulated solitary waves for the full-dispersion Kadomtsev--Petviashvilii (FDKP) equation with weak surface tension. The resulting waves are small-order perturbations of scaled, ... -
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 pseudo-differential 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, ... -
Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation
Ehrnstrom, Mats; Groves, Mark D (Journal article; Peer reviewed, 2018)The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number ). This equation admits—as an explicit solution—a 'fully localised' or 'lump' solitary ... -
Smooth stationary water waves with exponentially localized vorticity
Ehrnstrom, Mats; Walsh, Samuel; Zeng, Chongchun (Peer reviewed; Journal article, 2020)We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. A great deal of recent ... -
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 solitary-wave solutions to a nonlocal shallow-water wave model. An exponential decay result for supercritical solitary-wave solutions is given. Moreover, it is ...