Global small data radial symmetric solutions of 3D semilinear Euler-Poisson-Darboux equations

For the 3D semilinear Euler-Poisson-Darboux equation $\square u+\fracμ{t}\partial_tu=|u|^p$, where $t\geq1$, $μ>0$ and $p>1$, it is conjectured that there is a critical exponent $p_{crit}(3,μ)=\max\{p_s(3+μ), p_f(3)\}$ with the Strauss exponent $p_s(3+μ)=\frac{μ+4+\sqrt{μ^2+16μ+32}}{2(μ+2)}$ and the