scholarly journals A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating Kerr black hole

2012 ◽  
Vol 5 (3) ◽  
pp. 553-625 ◽  
Author(s):  
Jonathan Luk
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Vector Field ◽  
Kerr Black Hole ◽  
Field Method ◽  
Vector Field Method ◽  
Method Approach

Global solutions of quasilinear wave-Klein–Gordon system in two-space dimension: Technical tools

2017 ◽  
Vol 14 (04) ◽  
pp. 591-625 ◽  
Author(s):  
Yue Ma
Keyword(s):  
Wave Equation ◽  
Vector Field ◽  
Space Dimension ◽  
Gordon Equation ◽  
Global Solutions ◽  
Field Method ◽  
Time Dimension ◽  
Klein Gordon ◽  
Vector Field Method ◽  
Klein Gordon Equation

In this paper and its successor, we make an application of the hyperboloidal foliation method in [Formula: see text] space-time dimension. After the establishment of some technical tools in this paper, we will prove further the global existence of small regular solution to a class of hyperbolic system composed by a wave equation and a Klein–Gordon equation with null couplings. Our method belongs to vector field method and, more precisely, is a combination of the normal form and the hyperboloidal foliation method.

scholarly journals A vector field method for radiating black hole spacetimes

2020 ◽  
Vol 13 (1) ◽  
pp. 29-92 ◽  
Author(s):  
Jesús Oliver ◽  
Jacob Sterbenz
Keyword(s):  
Black Hole ◽  
Vector Field ◽  
Field Method ◽  
Black Hole Spacetimes ◽  
Vector Field Method

scholarly journals Modified Vector Field Path-Following Control System for an Underactuated Autonomous Surface Ship Modelin the Presence of Static Obstacles

2021 ◽  
Vol 9 (6) ◽  
pp. 652
Author(s):  
Haitong Xu ◽  
Miguel A. Hinostroza ◽  
C. Guedes Guedes Soares
Keyword(s):  
Control System ◽  
Vector Field ◽  
Path Following ◽  
Field Method ◽  
Integrated System ◽  
Ship Model ◽  
Surface Ship ◽  
Path Following Control ◽  
Exponentially Stable ◽  
Vector Field Method

A modified path-following control system using the vector field method for an underactuated autonomous surface ship model is proposed in the presence of static obstacles. With this integrated system, autonomous ships are capable of following the predefined path, while avoiding the obstacles automatically. It is different from the methods in most published papers, which usually study path-following and obstacle collision avoidance, separately. This paper considers the coupled path following and collision avoidance task as a whole. Meanwhile, the paper also shows the heading control design method in the presence of static obstacles. To obtain a strong stability property, a nonlinear autopilot is designed based on the manoeuvring tests of the free-running ship model. The equilibrium point of the controller is globally exponentially stable. For the guidance system, a novel vector field method was proposed, and the proof shows the coupled guidance and control system is uniform semi-global exponentially stable (USGES). To prevent the obstacles near the predefined path, the proposed guidance law is augmented by integrating the repelling field of obstacles so that it can control the ship travel toward the predefined path through the obstacles safely. The repelling field function is given considering the obstacle shape and collision risk using the velocity obstacle (VO) algorithm. The simulations and ship model test were performed to validate the integrated system of autonomous ships.

scholarly journals A vector field method for relativistic transport equations with applications

2017 ◽  
Vol 10 (7) ◽  
pp. 1539-1612 ◽  
Author(s):  
David Fajman ◽  
Jérémie Joudioux ◽  
Jacques Smulevici
Keyword(s):  
Vector Field ◽  
Field Method ◽  
Transport Equations ◽  
Vector Field Method
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