相关论文: Weak-strong uniqueness for the Landau equation by …

We consider the spatially inhomogeneous Landau equation with soft potentials, including the case of Coulomb interactions. First, we establish the existence of solutions for a short time, assuming the initial data is in a fourth-order…

We consider the spatially inhomogeneous Landau equation with hard potentials (i.e. with $\gamma \in [0,1]$) on the whole space $\mathbb{R}^3$. We prove existence and uniquenss of solutions for a small time, assuming that the initial data is…

We describe a time-dependent functional involving the relative entropy and the $\dot{H}^1$ seminorm, which decreases along solutions to the spatially homogeneous Landau equation with Coulomb potential. The study of this monotone functionial…

In this manuscript we investigate the regularization of solutions for the spatially homogeneous Landau equation. For moderately soft potentials, it is shown that weak solutions become smooth instantaneously and stay so over all times, and…

We consider weak solutions of the spatially inhomogeneous Landau equation with hard potentials ($\gamma \in (0,1]$), under the assumption that mass, energy, and entropy densities are under control. In this regime, with arbitrary initial…

We present a weak-strong uniqueness result for the inhomogeneous Navier-Stokes (INS) equations in $\mathbb{R}^d$ ($d=2,3$) for bounded initial densities that are far from vacuum. Given a strong solution within the class employed in Paicu,…

We establish the well-posedness and some quantitative stability of the spatially homogeneous Landau equation for hard potentials, using some specific Monge-Kantorovich cost, assuming only that the initial condition is a probability measure…

We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis…

We study the derivation of the spatially homogeneous Landau equation from the mean-field limit of a conservative $N$-particle system, obtained by passing to the grazing limit on Kac's walk in his program for the Boltzmann equation. Our…

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position…

We investigate in this work the rate of convergence to equilibrium of solutions to the spatially homogeneous Landau equation with soft potentials. Firstly, we prove a polynomial in time convergence using an entropy method with some new a…

We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact…

We consider the homogeneous Landau equation with Coulomb potential and general initial data $f_{in} \in L^p$, where $p$ is arbitrarily close to $3/2$. We show the local-in-time existence and uniqueness of smooth solutions for such initial…

We introduce a practical criterion that justifies the propagation and appearance of $L^{p}$-norms for the solutions to the spatially homogeneous Boltzmann equation with very soft potentials without cutoff. Such criterion also provides a new…

This paper addresses large-data local existence and uniqueness of classical solutions to the inhomogeneous Landau equation in the hard potentials case (including Maxwell molecules). Solutions have previously been constructed by Chaturvedi…

This work deals with the inhomogeneous Landau equation on the torus in the cases of hard, maxwellian and moderately soft potentials. We first investigate the linearized equation and we prove exponential decay estimates for the associated…

The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials $(-4\le \gm<0$), with and without angular cutoff. We prove the time-averaged $L^1$-convergence to…

Some peculiarities of the exploitation of the entropy inequality in case of weakly nonlocal continuum theories are investigated and refined. As an example it is shown that the proper application of the Liu procedure leads to the…

Weak-strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy. To overcome the difficulties caused by the molecular…

We establish a weak-strong uniqueness result for the isentropic compressible Euler equations, that is: As long as a sufficiently regular solution exists, all energy-admissible weak solutions with the same initial data coincide with it. The…