Local wellposedness in Sobolev space for the inhomogeneous non-resistive MHD equations on general domain

2017 ◽  
Vol 19 (06) ◽  
pp. 1650055
Author(s):  
Weiren Zhao
Keyword(s):  
Sobolev Space ◽  
Initial Data ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Mhd Equations ◽  
General Domain ◽  
Local Existence And Uniqueness ◽  
Uniqueness Of The Solution ◽  
Local Wellposedness

In this paper, we prove the local existence and uniqueness of the solution with discontinuous density for the inhomogeneous non-resistive magnetohydrodynamics (MHD) equations on a [Formula: see text] bounded domain [Formula: see text] or [Formula: see text], if the initial data [Formula: see text] with [Formula: see text] satisfies [Formula: see text].

Well-posedness and limit behaviors for a stochastic higher order modified Camassa–Holm equation

2016 ◽  
Vol 16 (06) ◽  
pp. 1650019
Author(s):  
Lin Lin ◽  
Guangying Lv ◽  
Wei Yan
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Higher Order ◽  
Well Posedness ◽  
Local Existence And Uniqueness ◽  
Holm Equation ◽  
The Cauchy Problem

This paper is devoted to the Cauchy problem for a stochastic higher order modified-Camassa–Holm equation [Formula: see text] The local existence and uniqueness with initial data [Formula: see text], [Formula: see text] and [Formula: see text], is established. The limit behaviors of the solution are examined as [Formula: see text].

scholarly journals Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system in the usual Sobolev space

1997 ◽  
Vol 40 (3) ◽  
pp. 563-581 ◽  
Author(s):  
Nakao Hayashi ◽  
Hitoshi Hirata
Keyword(s):  
Sobolev Space ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Initial Value ◽  
Hyperbolic Case ◽  
Local Existence And Uniqueness ◽  
Usual Sobolev Space

We study the initial value problem to the Davey-Stewartson system for the elliptic-hyperbolic case in the usual Sobolev space. We prove local existence and uniqueness H5/2 with a condition such that the L2 norm of the data is sufficiently small.

scholarly journals Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain

2011 ◽  
Vol 250 (3) ◽  
pp. 1719-1746 ◽  
Author(s):  
Igor Kukavica ◽  
Roger Temam ◽  
Vlad C. Vicol ◽  
Mohammed Ziane
Keyword(s):  
Euler Equations ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Local Existence And Uniqueness

scholarly journals Exponential decay of solutions with \(L^{p}\)-norm for a class to semilinear wave equation with damping and source terms

2020 ◽  
Vol 4 (2) ◽  
pp. 123-131
Author(s):  
Amar Ouaoua ◽  
◽  
Messaoud Maouni ◽  
Aya Khaldi ◽  
◽  
...  
Keyword(s):  
Wave Equation ◽  
Lyapunov Function ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Local Solution ◽  
Initial Value ◽  
Local Existence And Uniqueness ◽  
Decay Of Solutions ◽  
Uniqueness Of The Solution ◽  
Damping And Source Terms

In this paper, we consider an initial value problem related to a class of hyperbolic equation in a bounded domain is studied. We prove local existence and uniqueness of the solution by using the Faedo-Galerkin method and that the local solution is global in time. We also prove that the solutions with some conditions exponentially decay. The key tool in the proof is an idea of Haraux and Zuazua with is based on the construction of a suitable Lyapunov function.

scholarly journals Positive global solutions for a general model of size-dependent population dynamics

2000 ◽  
Vol 5 (3) ◽  
pp. 191-206 ◽  
Author(s):  
Nobuyuki Kato
Keyword(s):  
Growth Rate ◽  
Existence And Uniqueness ◽  
General Type ◽  
Local Existence ◽  
Global Solutions ◽  
Structured Population Models ◽  
Size Dependent ◽  
Structured Population ◽  
Local Existence And Uniqueness ◽  
Uniqueness Of The Solution

We study size-structured population models of general type which have the growth rate depending on the size and time. The local existence and uniqueness of the solution have been shown by Kato and Torikata (1997). Here, we discuss the positivity of the solution and global existence as well asL ∞solutions.

Periodic stochastic high-order Degasperis–Procesi equation with cylindrical fBm

2019 ◽  
Vol 19 (06) ◽  
pp. 1950043 ◽  
Author(s):  
Yong Chen ◽  
Hongjun Gao ◽  
Jianhua Huang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Time Variable ◽  
High Order ◽  
Hurst Parameter ◽  
Local Existence And Uniqueness ◽  
Uniqueness Of The Solution ◽  
Stochastic Term ◽  
Bourgain Space

This paper studies the periodic stochastic high-order Degasperis–Procesi (DP) equation driven by a cylindrical fractional Brownian motion (fBm) which is white in space. And it has the covariance with Hurst parameter [Formula: see text] in the time variable. The local existence and uniqueness of the solution [Formula: see text] in [Formula: see text] with [Formula: see text] are proved by fixed point theorem combined with the stochastic term estimations in the Besov-type Bourgain space [Formula: see text] and the second iteration of non-linear term.

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