ﻻ يوجد ملخص باللغة العربية
We consider the 1D transport equation with nonlocal velocity field: begin{equation*}label{intro eq} begin{split} &theta_t+utheta_x+ u Lambda^{gamma}theta=0, & u=mathcal{N}(theta), end{split} end{equation*} where $mathcal{N}$ is a nonlocal operator. In this paper, we show the existence of solutions of this model locally and globally in time for various types of nonlocal operators.
We consider the porous medium equation with a power-like reaction term, posed on Riemannian manifolds. Under certain assumptions on $p$ and $m$ in (1.1), and for small enough nonnegative initial data, we prove existence of global in time solutions, p
We prove the equivalence between the notion of Wasserstein gradient flow for a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian potential on one side, and the notion of entropy solution of a Burgers-type scalar conservation
In this paper, we are concerned with the global existence and blowup of smooth solutions of the 3-D compressible Euler equation with time-depending damping $$ partial_trho+operatorname{div}(rho u)=0, quad partial_t(rho u)+operatorname{div}left(rh
We study a multi-dimensional nonlocal active scalar equation of the form $u_t+vcdot abla u=0$ in $mathbb R^+times mathbb R^d$, where $v=Lambda^{-2+alpha} abla u$ with $Lambda=(-Delta)^{1/2}$. We show that when $alphain (0,2]$ certain radial solution
In this paper, we investigate the nonhomogeneous boundary value problem for the steady Navier-Stokes equations in a helically symmetric spatial domain. When data is assumed to be helical invariant and satisfies the compatibility condition, we prove t