4 papers · 1 filter
Non-unique solutions to the periodic gKdV equation
Nicholas Gismondi, Kunyi, Ma +2
In this paper we utilize a convex integration scheme to construct non-trivial weak solutions to the -generalized KdV equation which lie in $$ \bigcap_{ε> 0} C_t^0 L_x^{k-ε}([0…
Nontrivial integrable weak stationary solutions to active scalar equations with non-odd drift
Nicholas Gismondi
In this paper we construct nontrivial weak solutions to a class of stationary active scalar equations with a non-odd nonlocal operator in the drift term using a convex integration…
Intermittent solutions of the stationary 2D surface quasi-geostrophic equation
Nicholas Gismondi, Alexandru F. Radu
In this paper we construct non-trivial solutions to the stationary dissipative surface quasi-geostrophic equation on the two dimensional torus which lie strictly below the critical…
Intermittent singular solutions of the stationary 2D Navier-Stokes equations in sharp Sobolev spaces
Estepan Ashkarian, Ataleshvara Bhargava, Nicholas Gismondi +1
In this paper we construct non-trivial solutions to the stationary Navier-Stokes equations on the two dimensional torus which lie in $\bigcap_{ε\in (0,1)} L^{2-ε}(\mathbb{T}^2) \…