Perturbational blowup solutions to the compressible 1-dimensional Euler equations

We construct non-radially symmetry solutions for the compressible 1-dimensional adiabatic Euler equations in this Letter. In detail, we perturb the linear velocity with a drifting term:equation(1)u=c(t)x+b(t),u=c(t)x+b(t), to seek new solutions. Then, we transform the problem into the analysis of ordinary differential equations. By investigating the corresponding ordinary differential equations, a new class of blowup or global solutions can be given. Here, our constructed solutions can provide the mathematical explanations for the drifting phenomena of some propagation wave like Tsunamis. And when we adopt the Galilean-like transformation to a drifting frame, the constructed solutions are self-similar.

► We construct non-radially symmetry solutions for the 1-dimensional Euler equations. ► We perturb the linear velocity with a drifting term to seek new solutions. ► We transform the Euler system into the ordinary differential equations analysis. ► The solutions model the drifting phenomena of some propagation wave like Tsunamis. ► Under the Galilean-like transformation, the constructed solutions are self-similar.