19 citations · 50 across the 16 of their papers we have counts for
11 papers · 1 filter
Blow-up for energy supercritical defocusing nonlinear Schrödinger equations in dimensions three, four and five
Kevin Buck, Alvaro Carballeira, Javier Gómez-Serrano +1
We prove finite time blow-up from smooth, radial, compactly supported initial data for the energy supercritical defocusing nonlinear Schrödinger equation $i\partial_tu+Δu-|u|^{p-1}…
The regularity of the solutions to the Muskat equation: the degenerate regularity near the turnover points
Jia Shi
In this paper, we prove that if a solution to the Muskat problem with different densities and the same viscosity is sufficiently smooth, the solution is analytic in a region that d…
Non-radial implosion for compressible Euler and Navier-Stokes in and
Gonzalo Cao-Labora, Javier Gómez-Serrano, Jia Shi +1
In this paper we construct smooth, non-radial solutions of the compressible Euler and Navier-Stokes equation that develop an imploding finite time singularity. Our construction is…
Regularity of solutions to the Muskat equation
Jia Shi
In this paper, we show that if a solution to the Muskat problem in the case of different densities and the same viscosity is sufficiently smooth, then it must be analytic except at…
Existence of non-trivial non-concentrated compactly supported stationary solutions of the 2D Euler equation with finite energy
Javier Gómez-Serrano, Jaemin Park, Jia Shi
In this paper, we prove the existence of locally non-radial solutions to the stationary 2D Euler equations with compact support but non-concentrated around one or several points. O…
Long time stability of KAM tori for the nonlinear Schrödinger equation
Xiaolong He, Jia Shi, Xiaoping Yuan
In this paper, we prove the long time stability of KAM tori for the nonlinear Schrödinger equation on the torus with arbitrary dimensions.
A note on stability of Eliasson-Kuksin's KAM tori for the nonlinear Schrödinger equation
Xiaolong He, Jia Shi, Xiaoping Yuan
Eliasson and Kuksin developed a KAM approach to study the persistence of the invariant tori for nonlinear Schrödinger equation on . In this note, we improve Eliasso…
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…
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…
Infinite-time Exponential Growth of the Euler Equation on Two-dimensional Torus
Zhen Lei, Jia Shi
For any , we construct solutions to the two-dimensional incompressible Euler equations on the torus whose vorticity gradient grows exponentially in…