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math.AP2025
A monotonicity formula for the fractional Laplacian and instability results for the Shrira equation
Argenis J. Méndez, Oscar Riaño
By employing a new class of pseudo-differential operators introduced in a previous work, we establish a novel monotonicity formula for the fractional Laplacian in $\…
math.AP2025
Existence and uniqueness of radial solutions of semi-linear equations on manifolds
Nicolas Martinez-Alba, Oscar Riaño
We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold . By combining differential…
math.AP2025
On the decay of solutions for the negative fractional KdV equation
Alysson Cunha, Oscar Riaño, Ademir Pastor
We explore the limits of fractional dispersive effects and their incidence in the propagation of polynomial weights. More precisely, we consider the fractional KdV equation when a…