2024/09/30 by Alessio Pomponio, Pomponio, Alessio, Tatsuya Watanabe +1 · 2 citations
Mathematics · Physics and Astronomy · #Gas Dynamics and Kinetic Theory #Cosmology and Gravitation Theories #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2410.00189
This paper is devoted to the study of the nonlinear scalar field equation with a point interaction at the origin in dimensions two and three. By applying the mountain pass theorem and the technique of adding one dimensional space, we prove the existence of a nontrivial singular solution for a wide class of nonlinearities. We also establish the Pohozaev identity by proving a pointwise estimate of the gradient near the origin. Some qualitative properties of nontrivial solutions are also given.