Keyword

small initial data

Description: A condition in partial differential equations in which the initial state or data has sufficiently small size to support analysis of solution behavior.

Primary topic: Navier-Stokes equation solutions (40%)

OpenAlex ID: keywords/small-initial-data

Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids

1983 · Akitaka Matsumura, Takaaki Nishida · Communications in Mathematical Physics · 779

Lectures on Nonlinear Hyperbolic Differential Equations

1997 · Lars Hörmander · 673

A Maximum Principle Applied to Quasi-Geostrophic Equations

2004 · Antonio Córdoba, Diego Córdoba · Communications in Mathematical Physics · 598

Global solutions of nonlinear hyperbolic equations for small initial data

1986 · Demetrios Christodoulou · Communications on Pure and Applied Mathematics · 526

Blow-up of solutions of nonlinear wave equations in three space dimensions

1979 · Fritz John · manuscripta mathematica · 494

The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids

1979 · Akitaka Matsumura, Takaaki Nishida · Proceedings of the Japan Academy Series A Mathematical Sciences · 478

PDF

Systems of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Magnetohydrodynamics

1984 · Shuichi Kawashima · Institutional Repositories DataBase (IRDB) · 434

On hydrodynamics of viscoelastic fluids

2005 · Fang‐Hua Lin, Chun Liu, et al. · Communications on Pure and Applied Mathematics · 391

Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions

2004 · L. Corrias, B. Perthame, et al. · Milan Journal of Mathematics · 349

The problem of a self-gravitating scalar field

1986 · Demetrios Christodoulou · Communications in Mathematical Physics · 321

Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data

1985 · P. Degond, C. Bardos · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 302

PDF

Asymptotics for large time of solutions to the nonlinear Schrödinger and Hartree equations

1998 · Nakao Hayashi, Pavel I. Naumkin · American Journal of Mathematics · 299

Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces

2014 · Xinru Cao · Discrete and Continuous Dynamical Systems · 270

PDF

On nonlinear Schrödinger equations, II.H S -solutions and unconditional well-posedness

1995 · Tosio Kato · Journal d Analyse Mathématique · 251

Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations

2013 · Myeongju Chae, Kyungkeun Kang, et al. · Communications in Partial Differential Equations · 245

PDF

Strong solutions of the Navier-Stokes equation in Morrey spaces

1992 · Tosio Kato · Bulletin of the Brazilian Mathematical Society New Series · 242

Almost global wellposedness of the 2-D full water wave problem

2009 · Sijue Wu · Inventiones mathematicae · 233

PDF

Stochastic Navier-Stokes Equations

1995 · A. Bensoussan · Acta Applicandae Mathematicae · 223

Global wellposedness of the 3-D full water wave problem

2010 · Sijue Wu · Inventiones mathematicae · 222

Existence and Uniqueness of the Solution to the Dissipative 2D Quasi-Geostrophic Equations in the Sobolev Space

2004 · Ning Ju · Communications in Mathematical Physics · 220

Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data

1992 · G. Rein, A. D. Rendall · Communications in Mathematical Physics · 210

A New Bernstein’s Inequality and the 2D Dissipative Quasi-Geostrophic Equation

2007 · Qionglei Chen, Changxing Miao, et al. · Communications in Mathematical Physics · 209

PDF

On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics

2014 · Dongho Chae, Jihoon Lee · Journal of Differential Equations · 186

Nonlinear Wave Equations, Formation of Singularities

1990 · Fritz John · University lecture series · 182

On the temporal decay for the Hall-magnetohydrodynamic equations

2013 · Dongho Chae, Maria Schonbek · Journal of Differential Equations · 166

PDF

Works count: 2,588

Citation count: 35,580