اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCritical threshold for global regularity of Euler-Monge-Amp`ere system with radial symmetry
76
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the global wellposedness of the Euler-Monge-Amp`ere (EMA) system. We obtain a sharp, explicit critical threshold in the space of initial configurations which guarantees the global regularity of EMA system with radially symmetric initial data. The result is obtained using two independent approaches -- one using spectral dynamics of Liu & Tadmor [Comm. Math. Physics 228(3):435-466, 2002] and another based on the geometric approach of Brenier & Loeper [Geom. Funct. Analysis 14(6):1182--1218, 2004]. The results are extended to 2D radial EMA with swirl.
قيم البحث
اقرأ أيضاً
In this paper, the author studies quaternionic Monge-Amp`ere equations and obtains the existence and uniqueness of the solutions to the Dirichlet problem for such equations without any restriction on domains. Our paper not only answers to the open pr
oblem proposed by Semyon Alesker in [3], but also extends relevant results in [7] to the quaternionic vector space.
We prove the existence of entire solutions of the Monge-Amp`ere equations with prescribed asymptotic behavior at infinity of the plane, which was left by Caffarelli-Li in 2003. The special difficulty of the problem in dimension two is due to the glob
al logarithmic term in the asymptotic expansion of solutions at infinity. Furthermore, we give a PDE proof of the characterization of the space of solutions of the Monge-Amp`ere equation $det abla^2 u=1$ with $kge 2$ singular points, which was established by Galvez-Martinez-Mira in 2005. We also obtain the existence in higher dimensional cases with general right hand sides.
We obtain a genuine local $C^2$ estimate for the Monge-Amp`ere equation in dimension two, by using the partial Legendre transform.
We study a non-local hydrodynamic system with control. First we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then discuss t
he critical thresholds that leading to global regularity or finite-time blow-up of strong solutions in one and two dimensions. Finally we propose a finite volume scheme for numerical solutions of the controlled system. Several numerical simulations are shown to validate the theoretical and computational results of the paper.
A new proof for stability estimates for the complex Monge-Amp`ere and Hessian equations is given, which does not require pluripotential theory. A major advantage is that the resulting stability estimates are then uniform under general degenerations o
f the background metric in the case of the Monge-Amp`ere equation, and under degenerations to a big class in the case of Hessian equations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
