相关论文: On completeness of the Moutard transformations

Let $u$ be a nonnegative, local, weak solution to the porous medium equation for $m\ge2$ in a space-time cylinder $\Omega_T$. Fix a point $(x_o,t_o)\in\Omega_T$: if the average \[…

We study the set of invariant idempotent probabilities for place dependent idempotent iterated function systems defined in compact metric spaces. Using well-known ideas from dynamical systems, such as the Ma\~{n}\'{e} potential and the…

By the Moutard transformation method we construct two-dimensional Schrodinger operators with real smooth potential decaying at infinity and with a multiple positive eigenvalue. These potentials are rational functions of spatial variables…

We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that…

For manifolds with a distinguished asymptotically flat end, we prove a density theorem which produces harmonic asymptotics on the distinguished end, while allowing for points of incompleteness (or negative scalar curvature) away from this…

This paper concerns the Cauchy problem of the barotropic compressible Navier-Stokes equations on the whole two-dimensional space with vacuum as far field density. In particular, the initial density can have compact support. When the shear…

In this paper we consider the multi-dimensional Quantum Hydrodynamics (QHD) system, by adopting an intrinsically hydrodynamic approach. The present work continues the analysis initiated in [6] where the one dimensional case was studied.…

We study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations. For the two-phase Muskat problem, we establish global well-posedness and decay to…

We study the Cauchy problem for the relativistic Boltzmann equation near relativistic Maxwellians in the whole space. The purpose of this article is to handle hard potentials, and for initial data with finite $L^\infty$ norm, to construct…

We consider the Cauchy problem to the barotropic compressible Navier-Stokes equations. We obtain optimal local well-posedness in the sense of Hadamard in the critical Besov space $\mathbb{X}_p=\dot{B}_{p,1}^{\frac{d}{p}}\times…

We are concerned with nonnegative solutions to the Cauchy problem for the porous medium equation with a variable density $\rho(x)$ and a power-like reaction term $u^p$ with $p>1$. The density decays {\it fast} at infinity, in the sense that…

We consider a 3rd-order generalized Monge-Ampere equation u_yyy - u_xxy^2 + u_xxx u_xyy = 0 (which is closely related to the associativity equation in the 2-d topological field theory) and describe all integrable structures related to it…

We prove local boundedness of variational solutions to the double phase equation \begin{align*} \partial_t u +& P.V.\int_{\mathbb{R}^N}\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}}\\…

For the compressible Euler equations, even when the initial data are uniformly away from vacuum, solution can approach vacuum in infinite time. Achieving sharp lower bounds of density is crucial in the study of Euler equations. In this…

The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the…

The well-posedness of Cauchy problem of 3D compressible Euler equations is studied. By using Smith-Tataru's approach \cite{ST}, we prove the local existence, uniqueness and stability of solutions for Cauchy problem of 3D compressible Euler…

By using the Moutard transformation of two-dimensional Schroedinger operators we derive a procedure for constructing explicit examples of such operators with rational fast decaying potentials and degenerate $L_2$-kernels (this construction…

A new type of exact solvability is reported. We study the general central polynomial potentials (with 2q anharmonic terms) which satisfy the Magyari's partial exact solvability conditions (this means that they possess a…

The Muskat problem models the filtration of two incompressible immiscible fluids of different characteristics in porous media. In this paper, we consider both the 2D and 3D setting of two fluids of different constant densities and different…

We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate…