2 problems

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Large-time optimal-growth conjecture for free wave solutions with general $L^2$ data
Consider the free wave equation with initial data $u_0,u_1\in L^2$ and solution $u(t,\cdot)$ . The preceding result gives almost linear growth for data whose Fourier transform satis…
Conjectureopendispersive-equations large-time-asymptotics wave-equationsarXiv posted 2 days ago
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The $t^{-1/6}$ normalization conjecture for the stochastic heat equation
Normalization conjecture. The factor $t^{-\frac16}$ is the correct normalization, and the limit should satisfy an equation involving a weighted local time of the solution.
Conjectureopenlarge-time-asymptotics stochastic-analysis stochastic-heat-equationarXiv posted 2 days ago

Large-time optimal-growth conjecture for free wave solutions with general L2L^2L2 data