Partial Differential Equations and Applications

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Local well-posedness of the coupled Yang–Mills and Dirac system in temporal gauge
Partial Differential Equations and Applications - Tập 3 - Trang 1-23 - 2022
Hartmut Pecher
We consider the classical Yang–Mills system coupled with a Dirac equation in 3+1 dimensions in temporal gauge. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for small data with minimal regularity assumptions. This problem for smooth data was solved forty years ago by Y. Choquet-Bruhat and D. Christodoulou. The corresponding problem in Lorenz gauge wa...... hiện toàn bộ
Energy equality of MHD system under a weaker condition on magnetic field
Partial Differential Equations and Applications - Tập 4 - Trang 1-18 - 2023
Taichi Eguchi
We prove the energy equality of MHD system in the space founded by Cheskidov et al. (Nonlinearity 21:1233–1252, 2008) and Berselli and Chiodaroli (Nonlinear Anal 192:111704, 2020). It is clarified that the energy equality is established for a larger class of the magnetic field than that of velocity field. Most of the cases, we deal with the energy equality of MHD system in bounded domain. On the o...... hiện toàn bộ
Continuity of selected pullback attractors
Partial Differential Equations and Applications - Tập 2 - Trang 1-16 - 2021
Rodrigo A. Samprogna, Jacson Simsen
In this work we obtain theoretical results on continuity of selected pullback attractors for a generalized process and consider the continuity of attractors when the system is asymptotically autonomous. As an example, we apply the theory on a nonautonomous problem with reaction diffusion equations with dynamical boundary conditions, after that, with some additional hypotheses we consider the famil...... hiện toàn bộ
Regularity estimates for nonlocal equations with an asymptotic property
Partial Differential Equations and Applications - Tập 2 - Trang 1-13 - 2021
Disson dos Prazeres, Aelson Sobral
In this paper we obtain $${\mathcal {C}}^{1,(\sigma -1)^-}$$ regularity estimates for a class of nonlocal $${\mathcal {L}}_0(\sigma )-$$ uniformly elliptic equations with an asymptotic property. We...... hiện toàn bộ
Professor Dajun Guo: a true mathematician and educator
Partial Differential Equations and Applications - - 2020
Jin Sun, Xing‐Bin Pan, Yihong Du, Zhaoli Liu, Zhitao Zhang
Higher-order error estimates for physics-informed neural networks approximating the primitive equations
Partial Differential Equations and Applications - - 2023
Ruimeng Hu, Quyuan Lin, Alan Raydan, Sui Tang
Large-scale dynamics of the oceans and the atmosphere are governed by primitive equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is generally challenging. Neural networks have been shown to be a promising machine learning tool to tackle this challenge. In this work, we employ physics-informed neural networks (PINNs) to approximate the solutions to the PEs an...... hiện toàn bộ
Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime
Partial Differential Equations and Applications - Tập 3 - Trang 1-10 - 2021
Kimitoshi Tsutaya, Yuta Wakasugi
Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions. The blow-up condition is the same as in the accelerated expanding Friedmann–Lemaître–Robertson–Walker (FLRW) space...... hiện toàn bộ
On a hybrid continuum-kinetic model for complex fluids
Partial Differential Equations and Applications - Tập 3 - Trang 1-28 - 2022
A. Chertock, P. Degond, G. Dimarco, M. Lukáčová-Medvid’ová, A. Ruhi
In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic model. In particular, we combine conservation of mass and momentum for an isentropic macroscopic model with a kinetic representation of the microscopic behavior. After introducing a small scale of interest, we compute th...... hiện toàn bộ
Energy asymptotics for the strongly damped Klein–Gordon equation
Partial Differential Equations and Applications - Tập 3 - Trang 1-12 - 2022
Haidar Mohamad
We consider the strongly damped Klein–Gordon equation for defocusing nonlinearity and we study the asymptotic behaviour of the energy for periodic solutions. We prove first the exponential decay to zero for zero mean solutions. Then, we characterize the limit of the energy, when the time tends to infinity, for solutions with small enough initial data and we finally prove that such limit is not nec...... hiện toàn bộ
Calderón-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient
Partial Differential Equations and Applications - - 2022
Mouhamed Moustapha Fall, Tadele Mengesha, Armin Schikorra, Sasikarn Yeepo
Tổng số: 190   
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