Global solutions to the Hartree equation for large L^{p}-initial data

2019 ◽  
Vol 68 (4) ◽  
pp. 1149-1172
Author(s):  
Ryosuke Hyakuna
Keyword(s):  
Initial Data ◽  
Global Solutions ◽  
Hartree Equation

scholarly journals A remark on global solutions to random 3D vorticity equations for small initial data

2019 ◽  
Vol 24 (8) ◽  
pp. 4021-4030 ◽  
Author(s):  
Michael Röckner ◽  
◽  
Rongchan Zhu ◽  
Xiangchan Zhu ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Global Solutions ◽  
Small Initial Data ◽  
Vorticity Equations

Immediate smoothing and global solutions for initial data in L1 × W1,2 in a Keller–Segel system with logistic terms in 2D

2020 ◽  
pp. 1-21
Author(s):  
Johannes Lankeit
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Two Dimensional ◽  
Image Position

This paper deals with the logistic Keller–Segel model \[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ v_t = \Delta v - v + u \end{cases} \] in bounded two-dimensional domains (with homogeneous Neumann boundary conditions and for parameters χ, κ ∈ ℝ and μ > 0), and shows that any nonnegative initial data (u0, v0) ∈ L1 × W1,2 lead to global solutions that are smooth in $\bar {\Omega }\times (0,\infty )$ .

scholarly journals Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Pengpeng Ji ◽  
Chun Shen
Keyword(s):  
Initial Data ◽  
Riemann Problem ◽  
Phase Plane ◽  
Wave Interaction ◽  
Global Solutions ◽  
Geometrical Structures ◽  
Small Perturbations ◽  
Riemann Solutions ◽  
Piecewise Constant ◽  
Rarefaction Curves

The global solutions of the perturbed Riemann problem for the Leroux system are constructed explicitly under the suitable assumptions when the initial data are taken to be three piecewise constant states. The wave interaction problems are widely investigated during the process of constructing global solutions with the help of the geometrical structures of the shock and rarefaction curves in the phase plane. In addition, it is shown that the Riemann solutions are stable with respect to the specific small perturbations of the Riemann initial data.

scholarly journals Blow-Up of Solutions with High Energies of a Coupled System of Hyperbolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Jorge A. Esquivel-Avila
Keyword(s):  
Initial Data ◽  
Blow Up ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Coupled System ◽  
Initial Energy ◽  
Evolution System ◽  
High Energies ◽  
Second Order In Time

We consider an abstract coupled evolution system of second order in time. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We compare our results with those in the literature and show how we improve them.

Global solutions to a hyperbolic-parabolic coupled system with large initial data

2009 ◽  
Vol 29 (3) ◽  
pp. 629-641 ◽  
Author(s):  
Guo Jun ◽  
Xiao Jixiong ◽  
Zhao Huijiang ◽  
Zhu Changjiang
Keyword(s):  
Initial Data ◽  
Global Solutions ◽  
Coupled System ◽  
Large Initial Data

scholarly journals Absence of global solutions of a mixed problem for a Ginzburg–Landau type nonline-ar evolution equation

2019 ◽  
Vol 484 (2) ◽  
pp. 147-149
Author(s):  
Sh. M. Nasibov
Keyword(s):  
Initial Data ◽  
Evolution Equation ◽  
Mixed Problem ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Global Solutions ◽  
Ginzburg Landau

We study the problem of the absence of global solutions of the first mixed problem for one nonlinear evolution equation of Ginzburg–Landau type.We prove that global solutions of the studied problem are absent for “sufficiently large” values of the initial data.

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