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Inspired by the numerical evidence of a potential 3D Euler singularity\cite
{luo2014potentially, luo2013potentially-2}, we prove finite time blowup of the 2D Boussinesq …

We investigate the spectral instability of a 2 π/κ periodic Stokes wave of sufficiently small
amplitude, traveling in water of unit depth, under gravity. Numerical evidence suggests …

In this work we develop a computer-assisted technique for proving existence of periodic
solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit …

Inspired by the numerical evidence of a potential 3D Euler singularity [,], we prove finite time
singularity from smooth initial data for the HL model introduced by Hou-Luo in [,] for the 3D …

We study polynomial expansions of local unstable manifolds attached to equilibrium
solutions of parabolic partial differential equations. Due to the smoothing properties of …

This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We
present a method for validating blow-up solutions and their blow-up times, which is based …

We present numerical results and computer assisted proofs of the existence of periodic
orbits for the Kuramoto--Sivashinky equation. These two results are based on writing down …

We develop a theoretical framework for computer-assisted proofs of the existence of
invariant objects in semilinear PDEs. The invariant objects considered in this paper are …

In this paper, a general method to obtain constructive proofs of existence of periodic orbits in
the forced autonomous Navier–Stokes equations on the three-torus is proposed. After …