Browsing Institutt for matematiske fag by Author "Wang, Yuexun"
Now showing items 1-6 of 6
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A NOTE ON WELL-POSEDNESS OF BIDIRECTIONAL WHITHAM EQUATION
Pei, Long; Wang, Yuexun (Journal article; Peer reviewed, 2019)We consider the initial-value problem for the bidirectional Whitham equation, a system which combines the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow-water nonlinearity. ... -
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 ... -
Formation of singularities of spherically symmetric solutions to the 3D compressible Euler equations and Euler–Poisson equations
Hai-Liang, Li; Wang, Yuexun (Journal article; Peer reviewed, 2018)By introducing a new averaged quantity with a fast decay weight to perform Sideris's argument (Commun Math Phys, 1985) developed for the Euler Equations, we extend the formation of singularities of classical solution to ... -
Non-existence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier–Stokes Equations
Li, Hai-Liang; Wang, Yuexun; Xin, Zhouping (Journal article; Peer reviewed, 2018)The well-posedness of classical solutions with finite energy to the compressible Navier–Stokes equations (CNS) subject to arbitrarily large and smooth initial data is a challenging problem. In the case when the fluid density ... -
Solitary wave solutions to a class of Whitham?Boussinesq systems
Nilsson, Dag Viktor; Wang, Yuexun (Peer reviewed; Journal article, 2019)In this note, we study solitary wave solutions of a class of Whitham–Boussinesq systems which include the bidirectional Whitham system as a special example. The travelling wave version of the evolution system can be reduced ...