Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posedness [PDF]
, 2018 In this paper we analyse the well-posedness of the Cauchy problem for a rather general class of hyperbolic systems with space-time dependent coefficients and with multiple characteristics of variable multiplicity.
Christian Jah (7161323) +2 more
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Local and global well-posedness for nonlinear Dirac type equations [PDF]
, 2012 We investigate the local and global well-posedness of a variety of nonlinear Dirac type equations with null structure on R1+1. In particular, we prove global existence in L2 for a nonlinear Dirac equation known as the Thirring model. Local existence in
Candy, Timothy Lars
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Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation [PDF]
, 2018 This thesis is concerned with the well-posedness of the one-dimensional derivative non-linear Schrodinger equation (DNLS). In particular, we study the initial-value problem associated to DNLS with low-regularity initial data in two settings: (i) on the
Moşincat, Răzvan Octavian
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Low regularity well-posedness of the modified and the generalized Korteweg-de Vries equations [PDF]
, 2021 In this thesis, we study the well-posedness of the modified and generalized Korteweg-de Vries equations on the one-dimensional torus. We first consider the complex-valued modified Korteweg-de Vries equation (mKdV).
Chapouto, Andreia
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WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR p-EVOLUTION SYSTEMS OF PSEUDO-DIFFERENTIAL OPERATORS [PDF]
, 2013 We study p-evolution pseudo-differential systems of the first order with coefficients in (t,x) and real characteristics. We find sufficient conditions for the well-posedness of the Cauchy problem in H∞.
Ascanelli, Alessia, Boiti, Chiara
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Well-posedness of a model for water waves with viscosity [PDF]
, 2012 The water wave equations of ideal free–surface fluid mechanics are a fundamental model of open ocean movements with a surprisingly subtle well–posedness theory.
David Ambrose (7936688) +2 more
core +6 more sources
Persistence of global well-posedness for the 2D Boussinesq equations with fractional dissipation
Advances in Difference Equations, 2019 In this paper, we study the IBVP for the 2D Boussinesq equations with fractional dissipation in the subcritical case, and prove the persistence of global well-posedness of strong solutions.
Xing Su, Gangwei Wang, Yue Wang
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On global regularity of 2D generalized magnetohydrodynamic equations [PDF]
, 2013 In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are –ν(–Δ)αu and –κ(–Δ)βb. We show that smooth solutions are global in the following three cases: α≥1/2, β≥1; 0≤α≤1/2,
Tran, Chuong Van +2 more
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Global well-posedness to the incompressible Navier–Stokes equations with damping
Electronic Journal of Qualitative Theory of Differential Equations, 2017 We study the Cauchy problem of the 3D Navier–Stokes equations with nonlinear damping term $\alpha|\mathbf{u}|^{\beta-1}\mathbf{u}\ (\alpha>0\ \text{and}\ \beta\geq1)$. It is shown that the strong solution exists globally for any $\beta\geq1$.
Xin Zhong
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Global well-posedness of solutions for the epitaxy thin film growth model
Nonlinear Analysis, 2021 In this paper, we consider the global well-posedness of solutions for the initial-boundary value problems of the epitaxy growth model. We first construct the local smooth solution, then by combining some a priori estimates, continuity argument, the local
Ning Duan, Fengnan Liu, Xiaopeng Zhao
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