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8 papers · 2 filters
Structured Continuity Equations in Fibred Wasserstein Spaces
Benoît Bonnet-Weill, Nastassia Pouradier Duteil
In this article, we develop a comprehensive ODE-theory for structured continuity equations in fibred probability spaces, which represent a class of heterogeneous PDEs arising as th…
An all-topology two-fluid model for two-phase flows derived through Hamilton's Stationary Action Principle
Ward Haegeman, Giuseppe Orlando, Samuel Kokh +1
We present a novel multi-fluid model for compressible two-phase flows. The model is derived through a newly developed Stationary Action Principle framework. It is fully closed and…
Scattering of the 2D modified Zakharov-Kuznetsov equation
Philippe Anjolras
We study the modified Zakharov-Kuznetsov equation in dimension : \[ \partial_t u + \partial_x \left( Δu + u^3 \right) = 0 \] where $u : (t, (x, y)) \in \mathbb{R} \times \mathb…
On well-posedness for non-autonomous parabolic Cauchy problems with rough initial data
Hedong Hou
We establish a complete picture for existence, uniqueness, and representation of weak solutions to non-autonomous parabolic Cauchy problems of divergence type. The coefficients are…
Poincar{é}-Steklov operator and Calder{ó}n's problem on extension domains
Gabriel Claret, Michael Hinz, Anna Rozanova-Pierrat
We consider Calder{ó}n's problem on a class of Sobolev extension domains containing non-Lipschitz and fractal shapes. We generalize the notion of Poincar{é}-Steklov (Dirichlet-to-N…
Path-connectedness of incompressible Euler solutions
Philippe Anjolras
We study the incompressible Euler equation and prove that the set of weak solutions is path-connected. More precisely, we construct paths of Hölder regularity , valued in…