Related papers: Small scales and singularity formation in fluid dy…
This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 +…
We investigate the dynamics of Einstein equations in the vicinity of the two recently described types of singularity of anisotropic and homogeneous cosmological models described by the action $$ S=\int d^4x \sqrt{-g}{F(\phi)R -…
We review some recent results on the mean curvature flows of Lagrangian submanifolds from the perspective of geometric partial differential equations. These include global existence and convergence results, characterizations of first-time…
We introduce a rotation invariant short distance cut-off in the theory of an ideal fluid in three space dimensions, by requiring momenta to take values in a sphere. This leads to an algebra of functions in position space is non-commutative.…
To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from…
Nanofluidics has firmly established itself as a new field in fluid mechanics, as novel properties have been shown to emerge in fluids at the nanometric scale. Thanks to recent developments in fabrication technology, artificial nanofluidic…
A generalization of scalar electrodynamics called fluid electrodynamics is presented. In this theory a fluid replaces the Higgs scalar field. Fluid electrodynamics might have application to the theory of low temperature Helium superfluids,…
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…
Carroll hydrodynamics arises in the $c\to 0$ limit of relativistic hydrodynamics. Instances of its relevance include the Bjorken and Gubser flow models of heavy-ion collisions, where the ultrarelativistic nature of the flow makes the…
In this paper we investigate analytically the formation of finite time singularities in the three dimensional incompressible Euler equations under the model of Gibbon, Fokas, and Doering for vorticity stretching within a bounded cylindrical…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces…
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
We present a description of granular dynamics based on the idea of differentiation between fluid and solid components. First, we construct a model of completely fluidized phase. Then we discuss a shear surface motion on the boundary of the…
A system of equations for anisotropic hydrodynamics is derived that describes a mixture of anisotropic quark and gluon fluids. The consistent treatment of the zeroth, first and second moments of the kinetic equations allows us to construct…
We investigate the field equations in the Einstein-aether theory for static spherically symmetric spacetimes and a perfect fluid source and subsequently with the addition of a scalar field (with an exponential self-interacting potential).…
We propose a novel algorithm for the approximation of surface-quasi geostrophic (SQG) flows modeled by a nonlinear partial differential equation coupling transport and fractional diffusion phenomena. The time discretization consists of an…
We study the self-organization of turbulence in a geophysically motivated two-dimensional fluid with local interactions. Using simulations and theory, we show that the out-of-equilibrium flux to small scales imposes a constraint on the…
In this paper, the dynamics of spontaneous shape fluctuations of a single, giant quasi-spherical vesicle formed of a single lipid species is revisited theoretically. A coherent physical theory for the dynamics is developed based on a number…
The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding…