9 papers · 1 filter
Self-similar solutions for the Muskat equation
Eduardo García-Juárez, Javier Gómez-Serrano, Huy Q. Nguyen +1
We show the existence of self-similar solutions for the Muskat equation. These solutions are parameterized by ; they are exact corners of slope at and become s…
Remarks on stationary and uniformly-rotating vortex sheets: Flexibility results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we construct new, uniformly-rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via…
Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity , such that it has positive vo…
Any three eigenvalues do not determine a triangle
Javier Gómez-Serrano, Gerard Orriols
Despite the moduli space of triangles being three dimensional, we prove the existence of two triangles which are not isometric to each other for which the first, second and fourth…
Symmetry in stationary and uniformly-rotating solutions of active scalar equations
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we study the radial symmetry properties of stationary and uniformly-rotating solutions of the 2D Euler and gSQG equations, both in the smooth setting and the patch s…
Convexity of Whitham's highest cusped wave
Alberto Enciso, Javier Gómez-Serrano, Bruno Vergara
We prove the existence of a periodic traveling wave of extreme form of the Whitham equation that has a convex profile between consecutive stagnation points, at which it is known to…