We consider co-rotational wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere for $d\geq 3$ odd. This is an energy-supercritical model which is known to exhibit finite-time blowup via self-similar solutions. Based on a method developed by the second author and Schörkhuber, we prove the asymptotic nonlinear stability of the "ground-state" self-similar solution.
Exact, Rotational, Infinite Energy, Blowup Solutions to the 3-Dimensional Euler Equations
In this paper, we construct a new class of blowup solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations . In detail, we obtain a class of global rotational exact solutions for the compressible fluids with $γ>1$ :%} [c]{c}% ρ= \max \{ \frac{γ-1}{Kγ} [ C^{2}[ x^{2}% +y^{2}+z^{2}-(xy+yz+xz)] - \dot{a} (t)(x+y+z)+b(t)], 0\} ^{ \frac{1}{γ-1} } u_{1} =a(t)+C(y-z) u_{2} =a(t)+C(-x+z) u_{3} =a(t)+C(x-y). where a(t)= c_{0} + c_{1} t and b(t)=3 c_{0} c_{1} t+{3/2} c_{1} ^{2}t^{2}+ c_{2} % with $C$ , $c_{0}$ , $c_{1}$ and $c_{2}$ are arb…
Three self-similar solutions of Yang-Mills equations in high odd dimensions
Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）；Fakultät für Mathematik, Universität Bielefeld（比勒费尔德大学数学系）；Department of Mathematics, University of Michigan（密歇根大学数学系）
