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Nonlinear Analysis, ISSN 0362-546X, 11/2017, Volume 163, pp. 177 - 200
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 09/2016, Volume 33, Issue 5, pp. 1329 - 1352
The chemotaxis–Navier–Stokes system(0.1){nt+u⋅∇n=Δn−∇⋅(nχ(c)∇c),ct+u⋅∇c=Δc−nf(c),ut+(u⋅∇)u=Δu+∇P+n∇Φ,∇⋅u=0,(⋆) is considered under homogeneous boundary... 
Navier–Stokes | Global existence | Chemotaxis | EXISTENCE | MATHEMATICS, APPLIED | STABILIZATION | EQUATIONS | FLUID MODEL | NONLINEAR DIFFUSION | BLOW-UP | Navier-Stolces | Fluid dynamics
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 08/2017, Volume 159, pp. 181 - 207
We establish a weak–strong uniqueness principle for solutions to entropy-dissipating reaction–diffusion equations: As long as a strong solution to the... 
Reaction–diffusion equation | Mass-action kinetics | Weak–strong uniqueness | RENORMALIZED SOLUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | TRANSPORT | GLOBAL EXISTENCE | Weak-strong uniqueness | MASS | SYSTEMS | BLOWUP | Reaction diffusion equation
Journal Article
Annals of Mathematics, ISSN 0003-486X, 9/2018, Volume 188, Issue 2, pp. 577 - 684
We prove global existence of appropriate weak solutions for the compressible Navier–Stokes equations for a more general stress tensor than those previously... 
RENORMALIZED SOLUTIONS | global-weak solutions | non-monotone pressure laws | TRANSPORT-EQUATIONS | Compressible Navier-Stokes | vacuum state | anisotropic viscous stress | FINITE VOLUME SCHEME | DIFFERENTIAL-EQUATIONS | CAUCHY-PROBLEM | VECTOR-FIELDS | PART II | propagation of regularity | UNIQUENESS | MATHEMATICS | non-local terms | MAC SCHEME | transport equation
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 4/2019, Volume 70, Issue 2, pp. 1 - 27
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 12/2017, Volume 27, Issue 14, pp. 2745 - 2780
This paper deals with the Keller-Segel-Navier-Stokes system {n(t) +u .del(n) =Delta(n) - del.(nS(x,n,c). del c), c(t) +u .del(c) =Delta(c) - c+n, u(t)+(u .... 
Navier-Stokes | Chemotaxis | global existence | EXISTENCE | TENSOR-VALUED SENSITIVITY | MATHEMATICS, APPLIED | BOUNDEDNESS | NONLINEAR DIFFUSION | CHEMOTAXIS-FLUID EQUATIONS | ROTATIONAL FLUX | MODELS | CLASSICAL-SOLUTIONS | BLOW-UP | SATURATION
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 02/2019, Volume 29, Issue 2, pp. 209 - 235
The weak strong uniqueness for renormalized solutions to reaction-cross-diffusion systems in a bounded domain with no-flux boundary conditions is proved. The... 
Shigesada-Kawasaki-Teramoto model | renormalized solution | weak-strong uniqueness | relative entropy | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | FLUID | EQUATIONS | MEASURE-VALUED SOLUTIONS
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 10/2019, Volume 70, Issue 5, pp. 1 - 20
The present paper is concerned with the Maxwell–Landau–Lifshitz equation with spin accumulation under Dirichlet–Neumann boundary conditions in two-dimensional... 
Engineering | Mathematical Methods in Physics | 35K51 | Maxwell–Landau–Lifshitz equation | Spin accumulation | Global weak solutions | 82D40 | Theoretical and Applied Mechanics | 35Q61 | 35Q60 | EXISTENCE | Maxwell-Landau-Lifshitz equation | DIMENSIONS | MATHEMATICS, APPLIED
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 08/2017, Volume 159, pp. 339 - 364
We derive the global existence of weak solutions of the Shigesada–Kawasaki–Teramoto systems in any space dimension d≥1 with a rather general condition on the... 
Strongly coupled reaction diffusion system | Quasi-linear parabolic equations | Weak global attractor | MATHEMATICS, APPLIED | GLOBAL ATTRACTORS | EVOLUTION-EQUATIONS | IMPLICIT EULER SCHEME | MATHEMATICS | NONLINEAR CROSS-DIFFUSION | LONG-TIME STABILITY | PARABOLIC-SYSTEMS | NAVIER-STOKES EQUATIONS | DIFFUSION POPULATION-MODEL | ENTROPY
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2017, Volume 262, Issue 10, pp. 5271 - 5305
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2016, Volume 439, Issue 1, pp. 197 - 212
In this paper we study this chemotaxis-system{ut=Δu−χ∇⋅(u∇v)+g(u),x∈Ω,t>0,vt=Δv−v+u,x∈Ω,t>0, defined in a convex smooth and bounded domain Ω of Rn, with n≥1,... 
Logistic source | Global existence | Chemotaxis | Nonlinear parabolic systems | MATHEMATICS | MATHEMATICS, APPLIED | LOWER BOUNDS | EQUATIONS | BOUNDEDNESS | MODEL | ATTRACTOR | TIME BLOW-UP
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 10/2015, Volume 259, Issue 8, pp. 3730 - 3754
We consider an initial–boundary value problem for the incompressible chemotaxis-Navier–Stokes equations generalizing the porous-medium-type diffusion... 
Global existence | Navier–Stokes equation | Nonlinear diffusion | Chemotaxis | Navier-Stokes equation | EXISTENCE | MATHEMATICS | SENSITIVITY | BOUNDEDNESS | WELL-POSEDNESS | MODEL | FLUID EQUATIONS | Fluid dynamics
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 2015, Volume 336, Issue 2, pp. 581 - 617
This paper is devoted to a new integrable two-component Camassa-Holm system with peaked solitons (peakons) and weak-kink solutions. It is the first integrable... 
BOUNDARY VALUE-PROBLEMS | GLOBAL EXISTENCE | CAUCHY-PROBLEM | BLOW-UP PHENOMENA | WELL-POSEDNESS | WAVE-BREAKING | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATION | CONSERVATIVE SOLUTIONS | SHOCK-WAVES | HIERARCHY
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 06/2017, Volume 35, pp. 336 - 349
In this paper, we consider the Cauchy problem for the three dimensional chemotaxis-Navier–Stokes equations. By exploring the new a priori estimates, we prove... 
Global existence | Navier–Stokes | Weak solutions | Zygmund spaces | Chemotaxis | MATHEMATICS, APPLIED | BOUNDEDNESS | NONLINEAR DIFFUSION | WELL-POSEDNESS | KELLER-SEGEL SYSTEM | LOGISTIC SOURCE | Navier-Stokes | FLUID MODEL | BLOW-UP | Fluid dynamics | Information science
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 260, Issue 4, pp. 1132 - 1154
In this paper, we prove the existence of global weak solution for an integrable two-component Camassa–Holm shallow water system provided the initial data... 
Global existence | Weak solution | An integrable two-component Camassa–Holm shallow water system | An integrable two-component Camassa-Holm shallow water system | EXISTENCE | STABILITY | BREAKING WAVES | TRAJECTORIES | WELL-POSEDNESS | CIRCLE | MATHEMATICS | BOUNDARY VALUE-PROBLEMS | BLOW-UP PHENOMENA | EQUATION | PEAKONS
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 06/2018, Volume 114, pp. 191 - 210
This paper is dedicated to the construction of global weak solutions to the quantum Navier–Stokes equation, for any initial value with bounded energy and... 
Compressible quantum Navier–Stokes equations | Vacuum | Global weak solutions | Degenerate viscosity | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Compressible quantum | MODEL | Navier Stokes equations | Analysis of PDEs | Mathematics
Journal Article