A posteriori error estimates for self-similar solutions to the Euler equations. The main goal of this paper is to analyze a family of “simplest possible” initial data for which, as shown by numerical simulations, the incompressible Euler equations have multiple solutions. We take here a first step toward a rigorous validation of these numerical results. Namely, we consider the system of equations corresponding to a self-similar solution, restricted to a bounded domain with smooth boundary. Given an approximate solution obtained via a finite dimensional Galerkin method, we establish a posteriori error bounds on the distance between the numerical approximation and the exact solution having the same boundary data.
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References in zbMATH (referenced in 5 articles , 1 standard article )
Showing results 1 to 5 of 5.
- Bressan, Alberto; Shen, Wen: A posteriori error estimates for self-similar solutions to the Euler equations (2021)
- Ciampa, Gennaro; Crippa, Gianluca; Spirito, Stefano: Strong convergence of the vorticity for the 2D Euler equations in the inviscid limit (2021)
- Jeong, In-Jee: Loss of regularity for the 2D Euler equations (2021)
- Bressan, Alberto; Murray, Ryan: On self-similar solutions to the incompressible Euler equations (2020)
- Ciampa, Gennaro; Crippa, Gianluca; Spirito, Stefano: Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy (2020)