A New Flow on Open Manifolds: Short Time Existence and Uniqueness

2020 ◽  
Author(s):  
Jurgen Eichhorn ◽  
Hajar Ghahremani-Gol ◽  
Asadollah Razavi
Keyword(s):  
Existence And Uniqueness ◽  
Open Manifolds ◽  
Short Time ◽  
Time Existence

scholarly journals Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution

2006 ◽  
Vol 181 (3) ◽  
pp. 449-504 ◽  
Author(s):  
Olivier Alvarez ◽  
Philippe Hoch ◽  
Yann Le Bouar ◽  
Régis Monneau
Keyword(s):  
Existence And Uniqueness ◽  
Dislocation Dynamics ◽  
Uniqueness Of The Solution ◽  
Short Time ◽  
Time Existence

ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

2009 ◽  
Vol 19 (10) ◽  
pp. 1929-1957 ◽  
Author(s):  
P. A. MARKOWICH ◽  
N. MATEVOSYAN ◽  
J.-F. PIETSCHMANN ◽  
M.-T. WOLFRAM
Keyword(s):  
Free Boundary ◽  
Existence And Uniqueness ◽  
Price Formation ◽  
Equation Modeling ◽  
Boundary Equation ◽  
Uniqueness Of Solutions ◽  
One Dimensional ◽  
Time Extension ◽  
Short Time ◽  
Time Existence

We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results.

Existence and uniqueness theorems for the full three-dimensional Ericksen–Leslie system

2017 ◽  
Vol 27 (05) ◽  
pp. 807-843 ◽  
Author(s):  
Gregory A. Chechkin ◽  
Tudor S. Ratiu ◽  
Maxim S. Romanov ◽  
Vyacheslav N. Samokhin
Keyword(s):  
Existence And Uniqueness ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Periodic Case ◽  
Initial Value ◽  
Neumann Type ◽  
Type Boundary ◽  
Short Time ◽  
Time Existence ◽  
Leslie System

In this paper, we study the three-dimensional Ericksen–Leslie equations for the nematodynamics of liquid crystals. We prove short time existence and uniqueness of strong solutions for the initial value problem for the periodic case and in bounded domains with both Dirichlet- and Neumann-type boundary conditions.

scholarly journals Lorentz spaces in action on pressureless systems arising from models of collective behavior

2021 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha ◽  
Patrick Tolksdorf
Keyword(s):  
Initial Data ◽  
Collective Behavior ◽  
Existence And Uniqueness ◽  
Maximal Regularity ◽  
Parabolic Systems ◽  
Lorentz Spaces ◽  
Regularity Estimate ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

scholarly journals On the differential system govering flows in magnetic field with data inLp

1998 ◽  
Vol 21 (2) ◽  
pp. 299-305 ◽  
Author(s):  
Fengxin Chen ◽  
Ping Wang ◽  
Chaoshun Qu
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Boundary Conditions ◽  
Differential System ◽  
Existence And Uniqueness ◽  
Mhd Equations ◽  
The Earth ◽  
Initial And Boundary Conditions ◽  
Time Existence ◽  
The Magnetic Field

In this paper we study the system governing flows in the magnetic field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. For initial data in spaceLp, we obtained the local in time existence and uniqueness ofweak solutions of the system subject to appropriate initial and boundary conditions.

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