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Motivated by the work on stagnation-point type exact solutions (with infiniteenergy) of 3D Euler fluid equations by Gibbon et al. (1999) and the subsequentdemonstration of finite-time blowup by Constantin (2006) we introduce aone-parameter family of models of the 3D Euler fluid equations on a 2D symmetryplane. Our models are seen as a deformation of the 3D Euler equations whichrespects the variational structure of the original equations so that explicitsolutions can be found for the supremum norms of the basic fields. The value ofthe model's parameter determines if there is finite-time blowup, and thesingularity time can be computed explicitly in terms of the initial conditionsand the model's parameter. We use a representative parameter value, for whichthe solution blows up in finite-time, as a benchmark for the systematic studyof errors in numerical solutions. We compare numerical integrations of our"original" model with a "mapped" version of these equations. The mapped versionis a globally regular (in time) system of equations, obtained via a bijectivenonlinear mapping of time and fields from the original model equations(Bustamante 2011). We show that the mapped system's numerical solutionincreases accuracy in estimates of supremum norms and singularity time whileentailing only a small additional computational cost. We study the Fourierspectrum of the model's numerical solution and find that the analyticity-stripwidth (a measure of the solution's analyticity) tends to zero as a power law ina finite time. This is in agreement with the finite-time blowup of the supremumnorms, in the light of rigorous bounds stemming from the bridge (Bustamante &Brachet 2012) between the analyticity-strip method and the Beale-Kato-Majdatype of theorems. We conclude by discussing the implications of this researchon the analysis of numerical solutions of the 3D Euler fluid equations.

Symmetry-plane model of 3D Euler flows and mapping to regular systems to improve blowup assessment using numerical and analytical solutions