Add to ORKGWe consider the Cauchy problem for an equation of the form (∂t + ∂3x)u = F (u,ux,uxx) where F is a polynomial with no constant or linear terms and no quadratic uuxx term. For a polynomial nonlinearity with no quadratic terms, Kenig–Ponce–Vega proved local well-posedness in Hs for large s. In this paper, we prove local well-posedness in low regularity Sobolev spaces and extend the result to certain quadratic nonlinearities. The result is based on spaces and estimates similar to those used by Marzuola–Metcalfe– Tataru for quasilinear Schrödinger equations
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do...
Abstract In this article, we prove local well-posedness in low-regularity Sobolev spaces for general...
Abstract In this article, we prove local well-posedness in low-regularity Sobolev spaces for general...
We study some well-posedness issues of the initial value problem associated with the equation $...
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large ...
AbstractIn this article, we prove local well-posedness in low-regularity Sobolev spaces for general ...
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large ...
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large ...
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large ...
We establish local well-posedness in Sobolev spaces $H^s(\mathbb{T})$, with $s\geq -1/2$, for the in...
Abstract. We establish local well-posedness for arbitrarily large initial data in the usual Sobolev ...
In part I of this project we examined low-regularity local well-posedness for generic quasilinear Sc...
In part I of this project we examined low-regularity local well-posedness for generic quasilinear Sc...
AbstractWe establish local well-posedness for small initial data in the usual Sobolev spaces Hs(R), ...
AbstractIn this article, we prove local well-posedness in low-regularity Sobolev spaces for general ...
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do...
Abstract In this article, we prove local well-posedness in low-regularity Sobolev spaces for general...
Abstract In this article, we prove local well-posedness in low-regularity Sobolev spaces for general...
We study some well-posedness issues of the initial value problem associated with the equation $...
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large ...
AbstractIn this article, we prove local well-posedness in low-regularity Sobolev spaces for general ...
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large ...
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large ...
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large ...
We establish local well-posedness in Sobolev spaces $H^s(\mathbb{T})$, with $s\geq -1/2$, for the in...
Abstract. We establish local well-posedness for arbitrarily large initial data in the usual Sobolev ...
In part I of this project we examined low-regularity local well-posedness for generic quasilinear Sc...
In part I of this project we examined low-regularity local well-posedness for generic quasilinear Sc...
AbstractWe establish local well-posedness for small initial data in the usual Sobolev spaces Hs(R), ...
AbstractIn this article, we prove local well-posedness in low-regularity Sobolev spaces for general ...
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do...
Abstract In this article, we prove local well-posedness in low-regularity Sobolev spaces for general...
Abstract In this article, we prove local well-posedness in low-regularity Sobolev spaces for general...