On a New Type of Turbulence for Incompressible Magnetohydrodynamics

Abstract

1. By passing to the limit in a certain physical process we often obtain evolutionary partial differential equations in the space R ₊ × R ⁿ. And we want to know how small perturbations in initial conditions effect the prosses of passing to the limit with respect to ε which is assumed to be a small parameter. If a change of initial data by a value µø(x), x ∈ R ⁿ, (ø(x) is an entire bounded function independent of µ and ε) leads in time t < δ to a change of the solution by a value of order 1 (µ and δ are arbitrary small independent of ε), then the incorrectness (ill-posedness) is so strong that it cannot be regularised. This means that the passing to the limit is incorrect itself. Such incorrectness will be called the burst incorrectness.