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Small Scale Creation for 2D Free Boundary Euler Equations with Surface Tension
In this paper, we study the 2D free boundary incompressible Euler equations with surface tension, where the fluid domain is periodic in
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A Method for Finding Exact Solutions to the 2D and 3D Euler–Boussinesq Equations in Lagrangian Coordinates
We study the Boussinesq approximation for the incompressible Euler equations using Lagrangian description. The conditions for the Lagrangian fluid...
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The Stability and Decay for the 2D Incompressible Euler-Like Equations
This paper is concerned with the two-dimensional incompressible Euler-like equations. More precisely, we consider the system with only dam** in the...
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Uniqueness of Positive Vorticity Solutions to the 2d Euler Equations on Singular Domains
We show that particle trajectories for positive vorticity solutions to the 2D Euler equations on fairly general bounded simply connected domains...
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Time Periodic Solutions Close to Localized Radial Monotone Profiles for the 2D Euler Equations
In this paper, we address for the 2D Euler equations the existence of rigid time periodic solutions close to stationary radial vortices of type
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Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations
We study the behavior of solutions to the incompressible 2 d Euler equations near two canonical shear flows with critical points, the Kolmogorov and...
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Burst of Point Vortices and Non-uniqueness of 2D Euler Equations
We give a rigorous construction of solutions to the Euler point vortices system in which three vortices burst out of a single one in a configuration...
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Regularity Criterion for the 2D Inviscid Boussinesq Equations
The question of whether the two-dimensional inviscid Boussinesq equations can develop a finite-time singularity from general initial data is a...
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On Stability and Instability of \(C^{1,\alpha }\) Singular Solutions to the 3D Euler and 2D Boussinesq Equations
Singularity formation of the 3D incompressible Euler equations is known to be extremely challenging (Majda and Bertozzi in Vorticity and...
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2D Voigt Boussinesq Equations
We consider a critical conservative Voigt regularization of the 2D incompressible Boussinesq system on the torus. We prove the existence and...
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Minimal Acceleration for the Multi-dimensional Isentropic Euler Equations
On the set of dissipative solutions to the multi-dimensional isentropic Euler equations, we introduce a quasi-order by comparing the acceleration at...
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On the Existence of Weak Solutions for the 2D Incompressible Euler Equations with In–Out Flow and Source and Sink Points
Well-posedness for the two dimensional Euler system with given initial vorticity is known since the works of Judovič. In this paper we show existence...
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Traveling Waves Near Couette Flow for the 2D Euler Equation
In this paper we reveal the existence of a large family of new, nontrivial and smooth traveling waves for the 2D Euler equation at an arbitrarily...
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Explicit Solutions to the 3D Incompressible Euler Equations in Lagrangian Formulation
We introduce many families of explicit solutions to the three dimensional incompressible Euler equations for nonviscous fluid flows using the...