Fluid equations
Regularity: L1 regularity for incompressible Navier-Stokes equations using Hardy spaces.
sima96
Asymptotic behavior: Long-term asymptotic behavior of solutions to PDEs, particularly for nonlinear convection-diffusion equations, incompressible Navier Stokes and measure valued vorticity equations in 2D and 3D.
cpde94 sima96 asns96 natma01
Wave equations
Dissipative evolution problems: Sharp estimates of energy decay for solutions to dissipative nonlinear second-order evolution equations.
pa92
Backward global solutions: Existence of global solutions for dissipative nonlinear wave equations, analyzing their behavior as they grow toward the past.
jmpa94
Elliptic equations
Nonlinear elliptic equations: Existence and nonexistence results for nonlinear equations involving the critical Sobolev exponent depending on the geometry of the domain. Based on PL Lions concentrated compactness methods.
aihp92
