Jia Shi

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math.AP2025

Non-radial implosion for compressible Euler and Navier-Stokes in $T^{3}$ and $R^{3}$

Gonzalo Cao-Labora, Javier GÃ³mez-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…

math.AP2025

A note on the existence of self-similar profiles of the hydrodynamic formulation of the focusing nonlinear SchrÃ¶dinger equation

Gonzalo Cao-Labora, Javier GÃ³mez-Serrano, Jia Shi +1

After performing the Madelung transformation, the nonlinear SchrÃ¶dinger equation is transformed into a hydrodynamic equation akin to the compressible Euler equations with a certai…

math.AP2024

Non-radial implosion for the defocusing nonlinear SchrÃ¶dinger equation in $T^{d}$ and $R^{d}$

Gonzalo Cao-Labora, Javier GÃ³mez-Serrano, Jia Shi +1

In this paper we construct smooth, non-radial solutions of the defocusing nonlinear SchrÃ¶dinger equation that develop an imploding finite time singularity, both in the periodic se…

Non-radial implosion for compressible Euler and Navier-Stokes in T3 and R3

A note on the existence of self-similar profiles of the hydrodynamic formulation of the focusing nonlinear SchrÃ¶dinger equation

Non-radial implosion for the defocusing nonlinear SchrÃ¶dinger equation in Td and Rd

Non-radial implosion for compressible Euler and Navier-Stokes in $T^{3}$ and $R^{3}$

Non-radial implosion for the defocusing nonlinear SchrÃ¶dinger equation in $T^{d}$ and $R^{d}$