arXiv subjects

Elliot Adamson

Publications and source records attributed to Elliot Adamson.

2 recordsLinked to original sources

arXiv2026

The Strauss conjecture for the wave equation with critical damping

The Strauss conjecture concerns wave equations with power-type nonlinearities and seeks the optimal range of powers that admit global solutions for all sufficiently nice and sufficiently small initial data. In three spatial dimensions, it is well known that small data global existence is available provided that the power $p>p_c(3)=1+\sqrt{2}$, where $p_c(n)$ denotes the critical power in $n$-spatial dimensions. In the current article, the analogous problem is considered for damped wave equations where the damping coefficient is at the critical scaling. When $a$ denotes the constant multiple applied to the damping term, it is shown that the corresponding critical power is $p_c(3+a)$ provided that $a$ is sufficiently small.

math.AP↗

arXiv2026

The Strauss conjecture for the wave equation with scattering damping

The focus of this article is to establish the existence portion of the Strauss conjecture for wave equations with spatially dependent scattering damping. In the current setting, the damping is not sufficiently strong to alter the critical Strauss exponent. In a subsequent study, the authors will consider the case of damping coefficients with critical decay where a shift of the Strauss exponent is expected. While several recent studies of the Strauss conjecture have relied upon weighted Strichartz estimates, here, instead, an approach that is based only on integrated local energy estimates, in particular those with both $r^p$ and ghost weights, is developed. This technique also applies to the problem for the free equation. Space-time Klainerman-Sobolev estimates provide the necessary decay to close the argument.

math.AP↗