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We show the lifespan of a strong solution to the incompressible 3D axially symmetric Euler system in R 3 can be arbitrarily large if the initial swirl is small enough. A precise lower bound of the lifespan, depending on the size of ‖ ∇ × (v 0 , θ e θ) ‖ L ∞ , is given. This extends the conclusion of Danchin (Proc Am Math Soc 141:1979–1993, 2012), in which the domain must be distant from the axis of symmetry. This may help us to have a better understanding of the nonlinear framework and the blowup mechanism inherent in the 3D axisymmetric Euler equations. [ABSTRACT FROM AUTHOR]

The flow of chemically reacting gaseous mixture is associated with a variety of phenomena and processes. We study the combined quasineutral and inviscid limit from the flow of chemically reacting gaseous mixture governed by Poisson equation to incompressible Euler equations with the ill-prepared initial data in the unbounded domain $$\mathbb {R}^2\times {\mathbb {T}}$$ . Furthermore, the convergence rates are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study the incompressible inviscid limit of the viscous two-fluid model in the whole space R 3 with general initial data in the framework of weak solutions. By applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of the densities and the velocity, we prove rigorously that the weak solutions of the compressible two-fluid model converge to the strong solution of the incompressible Euler equations in the time interval provided that the latter exists. Moreover, thanks to the Strichartz's estimates of linear wave equations, we also obtain the convergence rates. The main ingredient of this paper is that our wave equations include the oscillations caused by the two different densities and the velocity and we also give an detailed analysis on the effect of the oscillations on the evolution of the solutions. [ABSTRACT FROM AUTHOR]