1D Model for the 3D Magnetohydrodynamics

Article Mathematics, Applied

On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations

Jiajie Chen et al.

Summary: This study presents a novel analytical method to prove the finite time asymptotically self-similar blowup phenomenon for the De Gregorio model and generalized De Gregorio model. The strategy involves using dynamic rescaling equations to establish the stability analysis of approximate self-similar profiles, addressing the issue of finite time asymptotically self-similar singularity.

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2021)

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Article Mathematics, Applied

STABLE SELF-SIMILAR BLOW-UP FOR A FAMILY OF NONLOCAL TRANSPORT EQUATIONS

Tarek M. Elgindi et al.

Summary: This study explores a family of nonlocal problems that simulate transport and vortex stretching effects in the incompressible Euler equations, establishing stable self-similar blow-up near known self-similar solutions through modulation techniques.

ANALYSIS & PDE (2021)

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Article Mathematics, Applied

On the Slightly Perturbed De Gregorio Model on S1

Jiajie Chen

Summary: This study investigates the generalization of the Constantin-Lax-Majda model on a circle and analyzes its behavior for different values of a. It also identifies the transition point at a = 1, which corresponds to the De Gregorio model.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2021)

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Article Mathematics, Applied

Collapse Versus Blow-Up and Global Existence in the Generalized Constantin-Lax-Majda Equation

Pavel M. Lushnikov et al.

Summary: The study focuses on the finite-time singularity formation versus global existence for solutions to the generalized Constantin-Lax-Majda equation, highlighting the influence of parameter a. Various behaviors are identified for different values of a, such as singularity formation, complex singularities, and the existence of solutions.

JOURNAL OF NONLINEAR SCIENCE (2021)

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Article Mathematics, Applied