A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary con...

Exact Travelling Wave Solutions for Some Nonlinear Equations Arising in Biology and Engineering

In this paper, the Exp -function method with the aid of symbolic computational system is used to obtain the exact travelling wave and solitary solutions of the Fitzhugh-Nagumo (FN), Modified Liouville equations and bi-directional Kaup-Kupershmidt (bKK) equation (sixth-order nonlinear equation). An attempt has been made to show the capabilities and wide-range applications of the Exp -function me...

Exact solutions of nonlinear interval Volterra integral equations

Exact solutions of (3 +1)-dimensional nonlinear evolution equations

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

Remarks on L decay of solutions for the third-grade non-Newtonian fluid flows inR

*Correspondence: [email protected] School of Mathematical Science, Anhui University, Hefei, 230601, P.R. China Abstract This paper is concerned with the improved L2 decay for solutions of a class of the third-grade non-Newtonian fluid flows in R3. By developing the classic Fourier splitting methods, we prove the non-uniform decay of solutions when u0 ∈ L2(R3) and improve algebraic decay rates o...