Publications (32)
Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations
Engui Fan, Manwai Yuen
For the 2D and 3D Euler equations, their existing exact solutions are often in linear form with respect to variables x,y,z. In this paper, the Clarkson-Kruskal reduction method is…
Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System
Manwai Yuen
In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% Ï_{t}+k_{2}uÏ_{x}+(k_{1}+k_{2})Ïu_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3…
Stabilities for Euler-Poisson Equations with Repulsive Forces in R^N
Manwai Yuen
This article extends the previous paper in "M.W. Yuen, \textit{Stabilities for Euler-Poisson Equations in Some Special Dimensions}, J. Math. Anal. Appl. \textbf{344} (2008), no. 1,…
Analytical Blowup Solutions to the Isothermal Euler-Poisson Equations of Gaseous Stars in R^N
Manwai Yuen
This article is the continued version of the analytical blowup solutions for 2-dimensional Euler-Poisson equations in "M.W. Yuen, Analytical Blowup Solutions to the 2-dimensional I…
Perturbational Blowup Solutions to the 1-dimensional Compressible Euler Equations
Manwai Yuen
We study the construction of analytical non-radially solutions for the 1-dimensional compressible adiabatic Euler equations in this article. We could design the perturbational meth…
Exact, Rotational, Infinite Energy, Blowup Solutions to the 3-Dimensional Euler Equations
Manwai Yuen
In this paper, we construct a new class of blowup solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. In deta…