8 problems

The paper constructs a weak self-similar solution of the two-dimensional incompressible Euler equations for sufficiently small non-axisymmetric perturbations of the specified perio…

Let $M\subset\mathbb{R}^2$ be any simply connected domain such that the constant-vorticity Euler solution $u_*$ on $M$ has a single eddy, meaning that its streamfunction has a sing…

Forcing-independence conjecture. The large deviations principle for the system holds independently of the choice of the forcing $f\in L^2(0,T;H_0)$; equivalently, if an LDP holds f…

LDP under the weak Kato hypothesis. The statement of the main large-deviations theorem holds true if the strong Kato hypothesis is replaced with the weak Kato condition.

Asymptotic expansion conjecture. We conjecture that $U_{\ell}^{\mathrm{in}}$ admits an asymptotic expansion about infinity of the form

Let $(\rho,u,\theta)$ solve the compressible Navier–Stokes–Fourier system with viscosity and heat-conductivity parameters tending to zero, subject to the generalized Navier boundar…

Constant-$C_1$ conjecture. In both cases considered in the cited works, the constant $C_1$ can be taken equal to $1$.

Let ${\epsilon}$ be the parameter tending to zero in the inviscid fluid dynamic limit of the Boltzmann equation, and let ${\alpha}({\epsilon})$ be the accommodation coefficient. Su…