On symmetries and invariant solutions of a coupled KdV system with variable coefficients.
On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field.
On the associative Nijenhuis relation.
On the asymptotic behavior of the motion of a viscous, heat-conducting, one-dimensional real gas.
On the asymptotics of solutions to the second initial boundary value problem for Schrödinger systems in domains with conical points
In this paper, for the second initial boundary value problem for Schrödinger systems, we obtain a performance of generalized solutions in a neighborhood of conical points on the boundary of the base of infinite cylinders. The main result are asymptotic formulas for generalized solutions in case the associated spectrum problem has more than one eigenvalue in the strip considered.
On the behavior of a nonstationary Poiseuille solution as .
On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer.
On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity
On the binding of polarons in a mean-field quantum crystal
We consider a multi-polaron model obtained by coupling the many-body Schrödinger equation for N interacting electrons with the energy functional of a mean-field crystal with a localized defect, obtaining a highly non linear many-body problem. The physical picture is that the electrons constitute a charge defect in an otherwise perfect periodic crystal. A remarkable feature of such a system is the possibility to form a bound state of electrons via their interaction with the polarizable background....
On the blow up criterion for the 2-D compressible Navier-Stokes equations
Motivated by [10], we prove that the upper bound of the density function controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.
On the blow up phenomenon for the critical nonlinear Schrödinger equation in 1D
On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴
We characterize the dynamics of the finite time blow-up solutions with minimal mass for the focusing mass-critical Hartree equation with H¹(ℝ⁴) data and L²(ℝ⁴) data, where we make use of the refined Gagliardo-Nirenberg inequality of convolution type and the profile decomposition. Moreover, we analyze the mass concentration phenomenon of such blow-up solutions.
On the blow-up set for non-Newtonian equation with a nonlinear boundary condition.
On the blowup theory for the critical nonlinear Schrödinger equations
On the boundary conditions at the contact interface between a porous medium and a free fluid
On the Caginalp system with dynamic boundary conditions and singular potentials
This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in , the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in...
On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation
We consider a system of balance laws describing the motion of an ionized compressible fluid interacting with magnetic fields and radiation effects. The local-in-time existence of a unique smooth solution for the Cauchy problem is proven. The proof follows from the method of successive approximations.
On the Cauchy Problem for the Kadomstev-Petviashvili Equation.
On the Cauchy problem for the Yang-Mills field equations
On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations.