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Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation.

Shuji Machihara, Kenji Nakanishi, Tohru Ozawa (2003)

Revista Matemática Iberoamericana

In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space Hs. We prove the existence and uniqueness of global solutions for small data in Hs with s > 1...

Small solutions to nonlinear Schrödinger equations

Carlos E. Kenig, Gustavo Ponce, Luis Vega (1993)

Annales de l'I.H.P. Analyse non linéaire

Smooth static solutions of the spherically symmetric Vlasov-Einstein system

G. Rein, A. D. Rendall (1993)

Annales de l'I.H.P. Physique théorique

Smoothing effect of small analytic solutions to nonlinear Schrödinger equations

Nakao Hayashi (1992)

Annales de l'I.H.P. Physique théorique

Smoothing of dispersive waves

Walter A. Strauss (1993)

Journées équations aux dérivées partielles

Smoothing of dispersive waves

Thomas Kappeler (1992)

Journées équations aux dérivées partielles

Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid

Olivier Glass, Franck Sueur, Takéo Takahashi (2012)

Annales scientifiques de l'École Normale Supérieure

We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the Hölder space $C^{1, r}$ . In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of the body and of the domain). In particular for analytic boundaries the motion of the rigid body is analytic...

Smoothness properties of solutions to the nonlinear Stokes problem with nonautonomous potentials

Dominic Breit (2013)

Commentationes Mathematicae Universitatis Carolinae

We discuss regularity results concerning local minimizers $u : ℝ^{n} \supset Ω \to ℝ^{n}$ of variational integrals like $\begin{matrix} \int_{Ω} {F (\cdot, ε (w)) - f \cdot w} d x \end{matrix}$ defined on energy classes of solenoidal fields. For the potential $F$ we assume a $(p, q)$ -elliptic growth condition. In the situation without $x$ -dependence it is known that minimizers are of class $C^{1, α}$ on an open subset $Ω_{0}$ of $Ω$ with full measure if $q < p \frac{n + 2}{n}$ (for $n = 2$ we have $Ω_{0} = Ω$ ). In this article we extend this to the case of nonautonomous integrands. Of course our result extends to weak solutions of the corresponding nonlinear...

Solitary wave and other solutions for nonlinear heat equations

Anatoly Nikitin, Tetyana Barannyk (2004)

Open Mathematics

A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary wave solutions is described. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.