Related papers: Equivalence between duality and gradient flow solu…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we…
We propose a supersymmetric gradient flow in ${\cal N}=1$ SQCD in four dimensions. The flow equation is derived in the superfield formalism and is also given for component fields of the Wess-Zumino gauge in a gauge covariant manner. We find…
This talk gives an overview of the recently-formulated Fluid/Gravity correspondence, which was developed in the context of gauge/gravity duality. Mathematically, it posits that Einstein's equations (with negative cosmological constant) in…
The hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-valued solutions and discontinuous velocities. An…
The initial-boundary value problem for the density-dependent incompressible flow of liquid crystals is studied in a three-dimensional bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is…
We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…
We perform a systematic analysis of flow-like solutions in theories of Einstein gravity coupled to multiple scalar fields, which arise as holographic RG flows as well as in the context of cosmological solutions driven by scalars. We use the…
This paper establishes the existence and uniqueness of classical solutions to the steady Triple-Deck equations, which describe incompressible boundary layer flow over localized roughness at high Reynolds numbers. The triple-deck theory was…
This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals along flows defined by some nonlinear diffusion equations…
We study the existence and uniqueness of nontrivial stationary solutions to a nonlocal aggregation equation with quadratic diffusion arising in many contexts in population dynamics. The equation is the Wasserstein gradient flow generated by…
The present paper deals with the nonhomogeneous incompressible asymmetric fluids equations in dimension $d= 2,3$. The aim is to prove the unique global solvability of the system with only bounded nonnegative initial density and $H^{1}$…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
We consider a third order non-autonomous ODE that arises as a model of fluid accumulation in a two dimensional thin-film flow driven by surface tension and gravity. With the appropriate matching conditions, the equation describes the inner…
The gradient flow equation is derived in four-dimensional N=1 supersymmetric Yang-Mills theory in terms of the component field of the Wess-Zumino gauge. We show that the flow-time derivative and supersymmetry transformation that is naively…
Here we provide uniqueness of vanishing viscosity solutions to sub-Riemannian mean curvature flow problem, which was known only far from characteristic points or under special symmetry condition. We employ vanishing viscosity approach and…
We prove an existence result for solutions to the stationary Euler equations in a domain with nonsmooth boundary. This is an extension of a previous existence result in smooth domains by Alber (1992). The domains we consider have a boundary…
The dynamics of a self-gravitating ensemble of collisionless particles is modeled by the Nordstr\"om-Vlasov system in the framework of the Nordstr\"om scalar theory of gravitation. For this system in two space dimensions, integral…
We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle…
We derive a uniqueness and stability principle for surface diffusion before the onset of singularities. The perturbations, however, are allowed to undergo topological changes. The main ingredient is a relative energy inequality, which in…
On the flat torus in any dimension we prove existence of a solution to the TV Wasserstein gradient flow equation, only assuming that the initial density $\rho_0$ is bounded from below and above by strictly positive constants. This solution…