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We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying…

We describe a new type of dynamical model for hot gas in galaxy groups and clusters in which gas moves simultaneously in both radial directions. Circulation flows are consistent with (1) the failure to observe cooling gas in X-ray spectra,…

In this paper we study the Heat Flow on Metric Random Walk Spaces, which unifies into a broad framework the heat flow on locally finite weighted connected graphs, the heat flow determined by finite Markov chains and some nonlocal evolution…

We consider the mass concentration phenomenon for the $L^2$-critical nonlinear Schr\"odinger equations of higher orders. We show that any solution $u$ to $iu_{t} + (-\Delta)^{\frac\alpha 2} u =\pm |u|^\frac{2\alpha}{d}u$, $u(0,\cdot)\in…

We give a simple proof of Onsager's conjecture concerning energy conservation for weak solutions to the Euler equations on any compact Riemannian manifold, extending the results of Constantin-E-Titi and…

The motion of compressible, inviscid fluid under the constant pressure on a rotating sphere is studied. The hodograph equations for the corresponding Euler equation are presented. They provide us with the class of solutions of the Euler…

Analytical/quasi-analytical solutions are proposed for a steady, compressible, two-phase flow in mechanical equilibrium in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between a…

We consider the semilinear heat equation, to which we add a nonlinear gradient term, with a critical power. We construct a solution which blows up in finite time. We also give a sharp description of its blow-up profile. The proof relies on…

We study the heat flow in the loop space of a closed Riemannian manifold $M$ as an adiabatic limit of the Floer equations in the cotangent bundle. Our main application is a proof that the Floer homology of the cotangent bundle, for the…

In this paper, we study the limiting behavior of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow as $\gamma$ tends to one. We show that the limit solution forms the delta wave to the pressureless Euler…

We study classical heat conduction in a dissipative open system composed of interacting oscillators. By exactly solving a twisted Fokker-Planck equation which describes the full counting statistics of heat flux flowing through the system,…

Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our…

Results on elliptic flow and two-particle correlations in the semi-hard regime are presented.

The magnitude of anisotropic flow in a nucleus-nucleus collision is determined by the energy density field, $\rho(x,y,z)$, created right after the collision occurs. Specifically, elliptic flow, $v_2$, and triangular flow, $v_3$, are…

Heavy inertial particles transported by a turbulent flow are shown to concentrate in the regions where an advected passive scalar, such as temperature, displays very strong front-like discontinuities. This novel effect is responsible for…

This paper deals with the blow-up properties of the solutions of the semilinear heat equation

We introduce notions of dynamic gradient flows on time-dependent metric spaces as well as on time-dependent Hilbert spaces. We prove existence of solutions for a class of time dependent energy functionals in both settings. In particular we…

Critical fluctuations in fluids and fluid mixtures yield a nonanalytic asymptotic Ising-like critical thermodynamic behavior in terms of power laws with universal exponents. In polymer solutions, the amplitudes of these power laws depend on…

We consider the nonlinear Schr{\"o}dinger equation with double power nonlinearity. We extend the scattering result in [17] for all L 2-supercritical powers, specially, our results adapt to the cases of energy-supercritical nonlinearity.

Using stochastic thermodynamics, the properties of interacting linear chains subject to periodic drivings are investigated. The systems are described by Fokker-Planck-Kramers equation and exact (explicit) solutions are obtained for periodic…