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In this paper, we find various analytic (1+3)D solutions to relativistic ideal hydrodynamic equations based on embedding of known low-dimensional scaling solutions. We first study a class of flows with 2D Hubble Embedding, for which a…
The rotating shallow water equations with f-plane approximation and nonlinear bottom drag are a prototypical model for mid-latitude geophysical flow that experience energy loss through simple topography. Motivated by numerical schemes for…
We are interested in the gradient flow of a general first order convex functional with respect to the $L^1$-topology. By means of an implicit minimization scheme, we show existence of a global limit solution, which satisfies an…
We analyse conditions for an evolution equation with a drift and fractional diffusion to have a Holder continuous solution. In case the diffusion is of order one or more, we obtain Holder estimates for the solution for any bounded drift. In…
An iterative scheme is presented to solve analytically the relativistic fluid dynamics equations. The scheme is applied to longitudinal expansion, transversal symmetric and transversal asymmetric (triaxial) expansion as well. Within this…
The paper reports the recent results on application and extension of the matrix formulation of lagrangian hydrodynamic equations. The matrix approach is based on the notion of continuous deformation of infinitesimal material elements and…
We consider a new nonlocal formulation of the water-wave problem for a free surface with an irrotational flow based on the work of Ablowitz, Fokas, and Musslimani and presented in the recent work of Oliveras. The main focus of the short…
We consider hydrodynamics with non conserved number of particles and show that it can be modeled with effective fluid Lagrangians which explicitly depend on the velocity potentials. For such theories, the {}``shift symetry''…
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…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
Gravity currents are a ubiquitous density driven flow occurring in both the natural environment and in industry. They include: seafloor turbidity currents, primary vectors of sediment, nutrient and pollutant transport; cold fronts; and…
Environmental fluid circulations are very often characterized by analyzing the fate and behavior of natural and anthropogenic tracers. Among these tracers, age is taken as an ideal tracer which can yield interesting diagnoses, as for…
In the realm of relativistic astrophysics, the ideal equation of state with a constant adiabatic index provides a poor approximation due to its inconsistency with relativistic kinetic theory. However, it is a common practice to use it for…
The Reynolds transport theorem occupies a central place in fluid dynamics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid, and connected to its corresponding differential…
A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on ${\mathbb Z}^n$, where the jump rates are asymmetric and long-range of order…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has…
We study the two-dimensional gravity water waves with a one-dimensional interface with small initial data. Our main contributions include the development of two novel localization lemmas and a Transition-of-Derivatives method, which enable…