6 problems

Physical-manifold approximation conjecture. The physical manifold locally approximates the inertial manifold linearly at every point on the attractor.

Fractional differential equation systems may be nonlinear and non-autonomous, and an inertial manifold is a reduced finite-dimensional manifold intended to capture their long-time…

Let $u$ be a solution of the Kuramoto–Sivashinsky equation, let $v$ be the convolution of $u_x$ with a normalized Gaussian in $x$ of standard deviation $2$, and define a stripe to…

Inertial-manifold obstruction conjecture. The absence of an inertial manifold is the only natural obstruction to the limit dynamics being finite-dimensional; equivalently, whenever…

An inertial manifold (IM) is a finite-dimensional, invariant, exponentially attracting manifold for the dynamics generated by a dissipative partial differential equation. Zelik's c…

Let $H$ be the phase space, let $H^2$ denote the more regular space, let $F$ be the non-linearity satisfying the reasonable assumptions considered in the paper, and let…