5 problems

Let $\Omega\subset\mathbb{R}^d$ be a bounded $\mathrm{C}^{1,\alpha}$-domain, and let $A_{1,\sigma,n}$ denote the Stokes operator with no-slip boundary conditions on…

For the one-dimensional Navier–Stokes–Fourier system on the half-line with inflow boundary data in the subsonic region, consider the composite wave consisting of a degenerate bound…

For the three-dimensional axially symmetric steady incompressible cavity-flow free-boundary problem, determine whether the cavity solutions whose existence was established by Garab…

Let $D$ be an open disk centered at the origin. Let $z\in D$ and let $\mathbf{v}\in C^2(\overline{D}\backslash \\{z\\})$ be a bounded flow solving the Euler equations on…

Consider the steady two-dimensional Navier–Stokes equations with boundary conditions $\boldsymbol{u}^{*}$ and source term $\boldsymbol{f}$, and let $\boldsymbol{F}$ denote the net…